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人工智能

Artificial Intelligence

第一版出版于 2022 年

First edition published 2022

作者：CRC Press

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© 2022 Robert H. Chen 和 Chelsea Chen

© 2022 Robert H. Chen and Chelsea Chen

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Library of Congress Cataloguing-in-Publication Data

姓名：陈，罗伯特·H.，1947- 作家。| 陈，切尔西，作家。

Names: Chen, Robert H., 1947- author. | Chen, Chelsea, author.

书名：人工智能：为好奇的读者提供的介绍/作者：Robert H. Chen、Chelsea Chen。

Title: Artificial intelligence : an introduction for the inquisitive reader / authored by Robert H. Chen, Chelsea Chen.

描述：博卡拉顿：CRC Press，2022 年。| 包括书目参考和索引。

Description: Boca Raton : CRC Press, 2022. | Includes bibliographical references and index.

标识符：LCCN 2021055530（印刷本）| LCCN 2021055531（电子书）| ISBN 9781032103471（精装本）| ISBN 9781032101842（平装本）| ISBN 9781003214892（电子书）

Identifiers: LCCN 2021055530 (print) | LCCN 2021055531 (ebook) | ISBN 9781032103471 (hardback) | ISBN 9781032101842 (paperback) | ISBN 9781003214892 (ebook)

主题：LCSH：人工智能。

Subjects: LCSH: Artificial intelligence.

分类：LCC Q335 .C4845 2022（印刷版）| LCC Q335（电子书）| DDC 006.3--dc23/eng/20211116

Classification: LCC Q335 .C4845 2022 (print) | LCC Q335 (ebook) | DDC 006.3--dc23/eng/20211116

LC 记录可在https://lccn.loc.gov/2021055530上查阅

LC record available at https://lccn.loc.gov/2021055530

LC 电子书记录可在https://lccn.loc.gov/2021055531上找到

LC ebook record available at https://lccn.loc.gov/2021055531

ISBN: 978-1-032-10347-1 （精装）

ISBN: 978-1-032-10347-1 (hbk)

ISBN: 978-1-032-10184-2 (平装)

ISBN: 978-1-032-10184-2 (pbk)

ISBN: 978-1-003-21489-2 (电子文档)

ISBN: 978-1-003-21489-2 (ebk)

DOI：10.1201/9781003214892

DOI: 10.1201/9781003214892

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内容

Contents

1. 前言
2. Preface
3. 第一部分人工智能进入人类世界
4. PART I The Arrival of AI in the Human World
5. 第1章■游戏机
6. CHAPTER 1 ■ Game-Playing Machines
7. IBM 701
8. The IBM 701
9. 游戏机
10. Game-Playing Machines
11. IBM 深蓝
12. IBM Deep Blue
13. 谷歌 AlphaGo
14. Google AlphaGo
15. IBM 项目辩论者
16. IBM Project Debater
17. 多伦多/DeepMind Video Gamer
18. Toronto/DeepMind Video Gamer
19. IBM Watson 问答
20. IBM WatsonQA
21. 卡内基梅隆大学德州扑克玩家 Libratus
22. Carnegie-Mellon Texas Hold'em Player Libratus
23. 第2章■工作机
24. CHAPTER 2 ■ Working Machines
25. IBM 医师助理
26. IBM Physician's Assistant
27. 纽约大学癌症诊断
28. NYU Cancer Diagnostic
29. 冠状病毒攻击者
30. Coronavirus Attackers
31. 自动驾驶汽车
32. Self-Driving Cars
33. 装配线质量控制
34. Assembly Line Quality Control
35. 电脑程序员
36. Computer Programmers
37. 数字助理
38. Digital Assistants
39. 系外行星天文学家
40. Exoplanet Astronomer
41. 第3章■智力
42. CHAPTER 3 ■ Intelligence
43. 第4章■人工智能奇点
44. CHAPTER 4 ■ The AI Singularity
45. 第二部分人工智能基础设施
46. PART II The Artificial Intelligence Infrastructure
47. 第5章■硬件
48. CHAPTER 5 ■ Hardware
49. 计算机
50. The Computer
51. 第6章■软件
52. CHAPTER 6 ■ Software
53. 第7章■计算机通讯
54. CHAPTER 7 ■ Computer Communications
55. 第8章■开源软件
56. CHAPTER 8 ■ Open Source Software
57. 第三部分从上到下​
58. PART III From Top to Bottom
59. 第9章■自上而下的人工智能
60. CHAPTER 9 ■ Top-Down Artificial Intelligence
61. 日本第五代
62. Japan's Fifth Generation
63. 逻辑主义与直觉主义
64. Logicism Versus Intuitionism
65. 第10章■自下而上的人工智能
66. CHAPTER 10 ■ Bottom-Up Artificial Intelligence
67. 自动驾驶汽车
68. Autonomous Vehicles
69. 第11章■机器学习建模
70. CHAPTER 11 ■ Machine Learning Modeling
71. 第12章■马尔可夫链蒙特卡罗模拟
72. CHAPTER 12 ■ Markov Chain Monte Carlo Simulation
73. 蒙特卡罗和原子弹
74. Monte Carlo and the Atomic Bomb
75. 第四部分结构和操作
76. PART IV Structure and Operation
77. 第13章■人工神经网络
78. CHAPTER 13 ■ Artificial Neural Networks
79. 第14章■模式识别
80. CHAPTER 14 ■ Pattern Recognition
81. 第15章■参数化
82. CHAPTER 15 ■ Parameterization
83. 第16章■梯度下降
84. CHAPTER 16 ■ Gradient Descent
85. 第17章■反向传播
86. CHAPTER 17 ■ Backpropagation
87. 第18章■卷积神经网络
88. CHAPTER 18 ■ Convolutional Neural Networks
89. 第五部分进展​
90. PART V Progression
91. 第19章■交叉熵成本函数
92. CHAPTER 19 ■ The Cross-Entropy Cost Function
93. 第20章■超参数化
94. CHAPTER 20 ■ Hyperparameterization
95. 第21章■大数据
96. CHAPTER 21 ■ Big Data
97. 第22章■大规模并行处理
98. CHAPTER 22 ■ Massively Parallel Processing
99. 量子计算人工神经网络
100. Quantum Computing Artificial Neural Networks
101. 第六部分预测能力
102. PART VI Powers of Prediction
103. 第23章■预测分析
104. CHAPTER 23 ■ Predictive Analytics
105. 第24章■受限玻尔兹曼机
106. CHAPTER 24 ■ Restricted Boltzmann Machine
107. 第25章■协同过滤中的潜在因素
108. CHAPTER 25 ■ Latent Factors in Collaborative Filtering
109. 外星卫星发现
110. Exomoon Discovery
111. 第26章■支持向量机
112. CHAPTER 26 ■ Support Vector Machines
113. 计算化学
114. Computational Chemistry
115. 第27章■强化学习
116. CHAPTER 27 ■ Reinforcement Learning
117. 第28章■AlphaGo 和 Alphastar
118. CHAPTER 28 ■ AlphaGo and Alphastar
119. 视频游戏玩家
120. Video Gamer
121. 第29章■博弈论
122. CHAPTER 29 ■ Game Theory
123. 不完全信息
124. Imperfect Information
125. 第七部分自然语言处理
126. PART VII Natural Language Processing
127. 第30章■自上而下的语音识别
128. CHAPTER 30 ■ Top-Down Speech Recognition
129. 第31章■自下而上的语音识别
130. CHAPTER 31 ■ Bottom Up Speech Recognition
131. 冠状病毒疫苗
132. Coronavirus Vaccine
133. 第32章■语音合成
134. CHAPTER 32 ■ Speech Synthesis
135. 第八部分机器人世界
136. PART VIII The Robotworld
137. 第33章■机器人在工作
138. CHAPTER 33 ■ Robots at Work
139. 穿透战争迷雾
140. Penetrating the Fog of War
141. 工业机器人
142. Industrial Robots
143. 半导体芯片制造
144. Semiconductor Chip Manufacturing
145. 机器人农场工人
146. Robot Farm Workers
147. 机器人医疗保健提供者
148. The Robot Healthcare Provider
149. 机器人程序员
150. The Robot Coder
151. 第34章■机器人千禧一代
152. CHAPTER 34 ■ The Robot Millennial
153. 机器人计算机科学家
154. The Robot Computer Scientist
155. 机器人科学家
156. The Robot Scientist
157. 第35章■机器人的未来
158. CHAPTER 35 ■ The Robot Future
159. 战争中的机器人
160. Robots at War
161. 机器人爱因斯坦
162. The Robot Einstein
163. 后记
164. AFTERWORD
165. 关于作者
166. ABOUT THE AUTHORS
167. 附录：欧拉-拉格朗日方程
168. APPENDIX: THE EULER-LAGRANGE EQUATION
169. 参考书目
170. BIBLIOGRAPHY
171. 指数
172. INDEX

前言

Preface

我本书以“人机对决”的趣味竞赛（如 IBM Deep Blue 对决 Garry Kasparov 和 Google AlphaGo 对决 Lee Sedol）为例，讲述了人工智能 (AI) 的探索历程，但人工智能的真正意义在于机器算法背后的人类思想以及机器未来可能具备的能力。人工智能的发展始于机械计算，可以看作是计算机科学的兴起推动的技术自然进步。有了硬件、软件和通信技术，人们开始认真探索人们梦寐以求的“专家系统”，从纯逻辑为基础的“自上而下”机器开始，输入公理，输出数学定理，但由于纯逻辑本身的矛盾以及数据和计算机能力的缺乏，逻辑理论家被大数据和大规模并行处理机器所取代，即所谓的“自下而上”方法。

IN THIS BOOK, THE ADVENTURES IN THE QUEST FOR artificial intelligence (AI) are exemplified by the entertaining demonstrations of “man versus machine” competitions such as IBM Deep Blue versus Garry Kasparov and Google AlphaGo versus Lee Sedol, but the real significance of AI evolves from the human ideas behind the machines’ algorithms and what the machine may be capable of in the future. Starting with mechanical calculation, the development of artificial intelligence can be seen as a natural progression of technology abetted by the generation of computer science. With the hardware, software, and communications in hand, the quest for the long-dreamed of “expert system” began in earnest with the pure logic-based “top-down” machine where axioms go in and mathematical theorems come out, but because of the inherent contradictions in pure logic and lack of data and computer power, the Logic Theorist was replaced by Big Data and massively parallel processing machines, in the so-called “bottom-up” approach.

自下而上的人工智能模仿人类大脑的结构和模式识别能力，利用电激活的人工神经元在并行处理计算机中形成的人工神经网络中形成识别和“思考”的突触模式。突触模式由神经元激活的马尔可夫链模型产生，神经元根据训练集加权，这一过程称为参数化。向量微积分的梯度下降最小化了机器模式和基本事实之间的差异，使用微积分的链式法则反向传播差异提供了机器学习，超参数化可以微调机器“思考”过程的准确性和计算效率。

Bottom-up AI mimics the structure and pattern recognition capability of human brains with electrically activated artificial neurons forming synaptic patterns of recognition and “thought” in an artificial neural network formed in a parallel-processing computer. The synaptic patterns are produced by Markov chain modeling of neuron activation with the neurons weighted in accord with a training set in a process called parameterization. The gradient descent of vector calculus minimizes the difference between the machine patterns and the ground truth, backpropagating the differences using the chain rule of calculus provides the machine learning, and hyperparameterization fine-tunes the accuracy and computational efficiency of the machine’s “thinking” process.

卷积神经网络在计算机视觉中的应用，借助大数据和大规模并行处理，已经将机器视觉带入了工业和社会的几乎每个方面。

The example of convolutional neural network used in computer vision armed with Big Data and massively parallel processing has brought machine vision into almost every facet of industry and society.

预测分析人工智能几乎无处不在，尤其是在商业、科学、政治和军事领域。人工智能强化通过学习，机器无需事先了解游戏规则就能击败顶级人类视频游戏玩家，而在知识不完善的现实世界中，人工智能系统已经击败了德州扑克比赛中的最强者。

Predictive analytics AI is employed almost everywhere, especially critically in business, science, politics, and the military. AI reinforcement learning has produced machines that can best the top human video gamers without even a priori knowing the rules of the games being played, and in the real world of imperfect knowledge, AI systems have beaten the best in Texas Hold’em poker competition.

由于语音的模糊性和变化性，使用生成循环神经网络的自然语言处理可以根据之前说过或推断的内容来评估即时语音，是目前最有前途的方法。

Because of the ambiguities and vagaries of speech, natural language processing using generative recurrent neural networks that can assess immediate speech in terms of what was spoken or inferred before are presently the most promising approaches.

在人类与人工智能之间的差异这一主题中，描述了实现算法背后的基本思想和机器学习的过程，其中的关键问题是机器进行数学运算的能力。

The basic ideas behind the implementing algorithms and the processes enabling a machine to learn are described within the theme of the difference between human and artificial intelligence, with the touchstone question being the capability of machines to do mathematics.

然而，读者所需的能力只是基本的微积分，并且通过示例解释了人工智能算法的特定方程，以便那些从未学习过或早已忘记微积分的人可以轻松理解算法背后的思想，希望能激发对数学在人工智能中的作用的认识。

That ability required by the reader, however, is only basic calculus, and explanations of the particular equations for artificial intelligence algorithms are provided with examples so that for those who have never learned, or have long forgotten their calculus, the ideas behind the algorithms can be easily understood, hopefully kindling an appreciation of the role of mathematics in artificial intelligence.

至于形式，一些数学表达方法，例如粗体表示向量和花括号矩阵，只在需要清晰表达时才使用，因为它们的身份从上下文中显而易见。措辞和拼写采用美式风格，但使用英式标点符号，在句子中留下引号和括号，而它们只是句子的一部分，后果是暴露句号或逗号。

As for form, some methods of mathematical exposition, for example the boldface representations of vectors, and curly letter matrices are employed only when necessary for clarity, as their identities are evident from the context. Wording and spelling are in the American style but with British punctuation leaving quotes and parentheses inside sentences of which they are only a part, at the dreadful consequence of laying bare the period or comma.

仅介绍算法的设计，对于那些希望了解代码的人，可以参考相关文章，免费的代码托管平台和优秀的在线编程教程提供了极大的便利和实际的编码体验。

Only the designs of the algorithms are presented, for those wishing to know the code, referrals are made to the relevant articles, and free code hosting platforms and excellent online programming tutorials offer great convenience and hands-on coding experience.

作者要感谢 Taylor & Francis Publishing 的 Callum Fraser 的专业指导、Mansi Kabra 对手稿的专业处理以及提供出色批评建议的手稿审阅者。

The authors would like to thank Callum Fraser of Taylor & Francis Publishing for professional guidance, to Mansi Kabra for expert handling of the manuscript, and the reviewers of the manuscript who provided excellent critical suggestions.

我人工智能进入人类世界

I The Arrival of AI in the Human World

赫他有两个共同的名字，亚瑟·塞缪尔，出生并成长于美国中部堪萨斯州恩波利亚的一个中产阶级家庭，毕业于当地的恩波利亚学院，他看上去是一个在传统美国社会长大的普通年轻人。然而，和蔼可亲但生性谨慎的亚瑟·塞缪尔很快就被誉为一个不寻常的新领域的杰出人物。因为从恩波利亚毕业后，他的特殊才能使他进入了工程教育的堡垒麻省理工学院，为他提供了坚实的电气工程基础，然后进入了技术创新的源泉 AT&T 贝尔实验室，在那里他研究了改变整个世界的电信系统，以及对第二次世界大战胜利至关重要的雷达技术。

He was a man with two common first names, Arthur Samuel, born and raised in mid-America Emporia Kansas in a middle-class family, a graduate of the local College of Emporia, he appeared to be an ordinary young man brought up in a traditional American society. However, the genial but inherently cautious Arthur Samuel was soon to known as a man of great distinction in an unusual new realm. For from Emporia, his special talents allowed him to enter the citadel of engineering education MIT which provided him a sound electrical engineering basis, and thence to the fount of technical innovation AT&T Bell Labs where he worked on the telecommunications systems that transformed the whole world, and the radar technology critical to victory in World War II.

他的贡献十分重大，但他并未止步于此。战后，塞缪尔密切关注新技术的发展轨迹，来到伊利诺伊大学，研究巨型 ILLIAC 科学计算机。被 IBM 聘用后，他全身心投入到世界上第一台商用大型计算机的设计中，这台计算机很快就颠覆了世界各地的工业和教育。但就在那时，他提出了一个大胆的想法，这一想法将成为变革性技术的先驱，进一步颠覆了工业和几乎所有世界人民的生活。他的想法受到他回归平民本源的启发，他是一个“思考机器”的魔术师，玩着一个几乎每个美国人都知道和玩过的琐碎游戏。

His contributions were significant, but he was not done, for after the War, closely tracking the locus of new technology, Samuel arrived at the University of Illinois to work on the giant ILLIAC scientific computer, and after being recruited by IBM, he was immersed in the design the world's first commercial mainframe computers that were soon to disrupt industry and education all over the world. But it was then that he came up with an audacious idea that would be the precursor of a transformative technology that would further disrupt industry and the lives of almost all the peoples of the world. His idea was inspired by a return to his everyman roots as the conjurer of a “thinking machine” playing a trivial game known and played by almost everyone in America.

乌到目前为止，人工智能已经被用于玩游戏，如果只是为了证明机器可以思考，那么机器已经在特定领域的努力中超越了人类。有了这种能力，除了像Jeopardy这样的琐碎智力竞赛游戏，例如 WatsonQA 也可以提供更多有用的功能，例如，利用其从答案中了解问题的超强能力（这是诊断吗？），协助医生治疗和减轻痛苦，或者机器人医生甚至接管患者的整个医疗工作，同时为机器的所有者创造新的商机。

Up to this point, artificial intelligence has been used for playing games, if the idea is just to prove that machines can think, the machine has already surpassed humans in restricted domain endeavors. With that capability, aside from trivial quiz show games like Jeopardy, for instance WatsonQA could just as well provide more useful functions, for example given its supreme ability to know the question from the answer (is that diagnosis?), assisting physicians in the treatment and alleviation of suffering or robot physicians even taking over a patient's entire medical treatment, while at the same time creating new business opportunities for the machine's proprietors.

在类似《危险边缘》的医疗诊断游戏《医生的困境》中，曾经有一道答案：

In the Jeopardy-like medical diagnosis game Doctor's Dilemma, there was once an answer:

该综合征的特征是关节痛、腹痛、可触及的紫癜和肾炎沉积物

The syndrome characterized by joint pain, abdominal pain, palpable purpura, and a nephritic sediment

问题（当然）是“什么是Hanoch-Schonlein Purpura？”Jeopardy 中使用的相同游戏格式可由 WatsonQA 用于严肃且无疑非平凡的医学诊断中，这需要在诊断时了解问题。

The question is (of course) “What is Hanoch-Schonlein Purpura?” The same game format used in Jeopardy can be used by WatsonQA in serious and indubitably non-trivial medical diagnostics that requires knowing the question when you have the diagnosis.

一个人工智能机器真的有智能吗？“智能”的定义多种多样，且存在争议，其中最普遍的定义可能是：¹

Are AI machines really and truly intelligent? “Intelligence” has been variously and controversially defined, perhaps the most general being,¹

获取和应用知识和技能的能力

The ability to acquire and apply knowledge and skills

所有描述的游戏和工作机器都很容易满足这一定义的要素，因此，为了解决这个问题，认知心理学家又补充了²

All the game-playing and working machines described easily satisfy the elements of this definition, so coming to the rescue, cognitive psychologists have added,²

感知或推断信息并将其保留为知识以应用于环境或情境中的适应性行为的能力

The ability to perceive or infer information, and to retain it as knowledge to be applied towards adaptive behaviors within an environment or context

机器仍然可以轻松通过这一智力测试，因此，为了特别区分人类智力和动物智力，这些定义得到了以下支持：³

The machines can still easily pass this test of intelligence, so in an apparent attempt to ad hoc distinguish human intelligence from animal intelligence, these definitions have been buttressed with,³

理解、推理、批判性思维、计划、情感知识、创造力、意识和自我意识

understanding, reasoning, critical thinking, planning, emotional knowledge, creativity, consciousness, and self-awareness

“理解”、“推理”、“批判性思维”和“规划”显然有定义模糊的危险。“情感知识”的含义无人知晓，但如果它意味着对情感的感知在其他情况下，现代计算机视觉的面部情绪识别显然可以满足要求。

“Understanding”, “reasoning’, “critical thinking”, and “planning” clearly are in danger of circling definition. What is meant by “emotional knowledge” is anybody's guess, but if it means the perception of emotion in others, then modern computer vision's facial recognition of mood clearly fills the bill.

在创造力方面，AlphaGo在第二局比赛中的第37步“肩击”被一位专家评论员称赞为超越人类教学的真正创造性的原创举措^。4

As for creativity, AlphaGo's “shoulder hit” move 37 in the Game 2 has been lauded by an expert commentator as a truly creative original move beyond human teaching.⁴

李世石在赛前信心满满地预测“绝对胜利”，但AlphaGo的第37步却让他大吃一惊，称其为“天才的火花”，是人类创造力的标志。

Lee Sedol before the match had confidently predicted “total victory”, but he was astounded by AlphaGo's move 37, calling it a “spark of genius”, the hallmark of human creativity.

在第四局比赛中，李世石“神棋”78 后，AlphaGo 的表现有所下降，这或许表明机器对巨大挑战的情感认知，也可能是一种自我意识，即它没有适当的反应。事实上，与“失败概率”指数相称的玩游戏的计算机可以评估最终失败的可能性，并显示一个绝望的“认输”输出。

In Game 4, AlphaGo's performance declined after Lee Sedol's “divine wedge move” 78, perhaps an indication of a machine's emotional knowledge of a formidable challenge, and possibly a kind of self-awareness that it had no appropriate response. Indeed, game-playing computers commensurate with a “probability of loss” index, can assess the likelihood of ultimate defeat and display a forlorn “resign” output.

在输掉比赛之后，AlphaGo 有足够的时间恢复，并赢得了第五场比赛，其中的很多棋步被李世石描述为“奇怪的走法”，这可以看作是它能够识别对手的新走法、对其进行推理、在第四场比赛中批判性地思考自己的反应，以及随后为第五场比赛所做的计划，所有这些都表现出了敏锐的适应智能。

Given time to recover after the loss, AlphaGo went on to win Game 5 with many of what Lee Sedol later described as “weird moves”, which could be seen as acknowledging the opponent's new moves, reasoning about them, critical thinking of its responses in Game 4, and subsequent planning for Game 5, all evincing an acute adaptive intelligence.

在与 AlphaGo 的划时代对决之后，虽然受到了挫折，但如今更加强大的李世石在随后与人类围棋大师的所有比赛中都取得了胜利。李世石表示，与柯洁所担心的相反，李世石“从 AlphaGo 那里学到了东西”，并且“它改变了围棋未来的玩法”。也就是说，机器可以向超级专家人类传授一些新的东西，正如棋盘上的一句谚语所说，

After the epochal match with AlphaGo, a chastened, but now more formidable Lee Sedol went on to win all of his subsequent matches against human Go Masters, stating that conversely to what Ke Jie had feared, Lee Sedol “learned from AlphaGo”, and that “it has changed the way Go would be played in the future”. That is, the machine had something new to teach the supremely expert human in accord with the board game adage,

有时你给他们一个教训，有时他们给你一个教训。

Sometimes you give them a lesson, sometimes they give you a lesson.

剩下的就是增强智能定义中的意识和自我意识元素。意识可能只是大脑特定的神经元激活模式，这种模式在动物和人类身上自然发生，在计算机神经网络中则人工发生。

That leaves the consciousness and self-awareness elements of the augmented definition of intelligence to be addressed. Consciousness could be no more than a brain's particular neuron activation pattern, which occurs naturally in animals and humans and artificially in computer neural networks.

牛津数学物理学家罗杰·彭罗斯认为，实现某种认知是智能意识的瞬间。例如，在观看埃舍尔著名的《天使与恶魔，通常首先是恶魔，然后在突然的感知闪现中，天使也被辨别出来，进一步的观察表明，分形是永无止境的，永远延伸到无穷大。在观察图画时，每一步新的认识都构成了一种新的意识，从而形成了一种新的意识智慧^。5

Oxford mathematical physicist Roger Penrose has suggested that the realization of a particular recognition is an instant of intelligent consciousness. For example, when viewing Escher's famous Angels and Demons, typically first the demons, and then in a sudden flash of perception, the angels are also discerned, and further observation reveals that the fractal is never-ending, extending forever to infinity. In observing the drawing, each new step of recognition constitutes a new awareness and thus a newly conscious intelligence.⁵

在视觉错觉中，人类永远无法知道何时可以识别错觉；然而，在机器模式识别中，错觉的决策概率应该是相等的，这意味着如果错觉是显而易见的，机器会立即知道有两种可能性，每种可能性都是 0.5，而人类必须等待有意识地意识到这些可能性，而有些人永远无法辨别不同的错觉。从这个意义上说，计算机视觉机器对可能性的感知更胜一筹。

In optical illusions, humans can never know when one may recognize the illusion; however, the decisional probability of the illusions should be equal in machine pattern recognition, which means that if an illusion is palpable, the machine will know at once that there are two possibilities, each at 0.5, while a human must wait for conscious awareness of the possibilities, and some humans will never be able to discern the different illusions. In this sense, the computer vision machine's perception of the possibilities is superior.

这表明人工神经网络的模式识别能力可以等同于甚至优于人类的模式识别能力，从而代表了与人类相似的意识和良知，能够满足认知心理学家对智能的定义中的那些要素。

This shows that an artificial neural network's pattern recognition capability can be equal or superior to human pattern recognition, and as such represents an awareness and consciousness similar to a human's that can satisfy those elements of the cognitive psychologist's definition of intelligence.

继续定义，自我意识是视频游戏中的非玩家角色（NPC）似乎拥有的东西，显然知道自己相对于代理玩家和游戏环境能够做什么，因此计算机程序以及驱动 NPC 的硬件和软件显然也具有一定程度的自我意识。但是，这仅仅是人类程序员设计的一种意识吗？也就是说，是创造机器的人实际上提供了机器所表现出的智能吗？

Continuing with the definition, self-awareness is something that a non-playing character (NPC in a video game appears to possess, apparently knowing what he/she/it is capable of vis à vis the agent-player and the game environment, so the computer program and the hardware and software that drives the NPC apparently also has some modicum of self-awareness. However, is that merely an awareness designed by the human programmer? That is, is it the human who created the machine actually providing the intelligence that the machine is apparently displaying?

人类一旦意识到并意识到一个概念，例如视觉错觉中存在两种相反的状态，就可以通过抽象推理概念来理清情况。许多人都同意数学是需要抽象推理的东西，而且几乎每个社会都对那些擅长数学的人的明显智慧怀有不安的敬意，这可能只是以最纯粹的形式进行抽象和逻辑推理的能力。数学的定义是：⁶

A human, once conscious and aware of a concept, for example the existence of two opposing states in an optical illusion, can sort out the situation by reasoning about the concepts in the abstract. Many can agree that mathematics is something that requires that abstract reasoning, and in almost every society there is an often uneasy respect for the very apparent intelligence of those who are good at mathematics, which may be just the ability to abstractly and logically reason in its purest form. A definition of mathematics is:⁶

一门以非常紧凑的形式，用逻辑的方式归纳和演绎研究概念之间的关系，直指问题的核心的学科

A discipline that logically investigates inductively and deductively the relationships among concepts in a very compact formthat gets to the heart of the matter

如果说智力有试金石的话，也许就是做数学的能力，正如许多人所相信的那样，这是人类抽象思维最纯粹的表现。做数学可以定义为

If there is a touchstone of intelligence, perhaps it is this ability to do mathematics, as many have believed, the purest manifestation of abstract human thought. Doing mathematics can be defined as

发现不同功能之间的关联方面，并得出一些合理的结论。

the discovery of relational aspects of disparate functions that can lead to some reasonable conclusion.

柏拉图认为数学不是人类发明的学科，而是一种存在于天体但控制着地球的以太逻辑，人类通过对数学形式的初步认识可以时不时地造访它；正如彭罗斯所解释的那样，数学概念和数学真理存在于一个现实世界中，这个世界是永恒的，没有不同于物理世界的物理位置，但从这个意义上讲，物理世界必须被理解，而且我们的思想可以通过对数学形式的“认识”和对它们进行推理的能力直接进入这个柏拉图领域。

Instead of a human-invented discipline, Plato for one saw mathematics as an æthereal logic residing in the Heavens but controlling the Earth, flittingly visited by mankind through an incipient awareness of mathematical forms; as Penrose explains it, mathematical concepts and mathematical truths inhabit an actual world of their own that is timeless and without physical location distinct from the physical world, but in terms of which the physical world must be understood and our minds do have some direct access to this Platonic realm through an “awareness” of mathematical forms, and our ability to reason about them.

伽利略认为宇宙是一本用数学语言写成的巨著，而彭罗斯认为只有人类才能进入柏拉图世界和伽利略的数学宇宙，因为这是一种高度专业化和独特的人类活动。事实上，正如彭罗斯所补充的那样，有些人可能会说这是一种仅限于某些特殊人类的活动。

Galileo believed that the Universe is a grand book written in the language of mathematics, and Penrose thought that only humans can access the Platonic world and Galilean Universe of mathematics as it is a highly specialized and peculiarly human activity. Indeed as Penrose added, some might say that it is an activity confined to certain peculiar humans.

人工智能先驱艾伦·纽厄尔和赫伯特·西蒙在兰德公司由约翰·肖于 1955 年编写的计算机程序中，解决了经典的心身问题：由无生命物质组成的机器是否能够具有有生命思维的思考能力。

The artificial intelligence pioneers Allen Newell and Herbert Simon in a computer program written by John Shaw in 1955 at the RAND Corporation confronted the classic mind-body problem of whether a machine composed of inanimate matter can have the thinking capability of an animate mind.

他们的逻辑理论家是第一个专门设计用来模拟人类思维解决问题的思考过程的计算机程序，并选择了证明数学定理这一深奥的学科作为试验场。它证明了阿尔弗雷德·诺思·怀特黑德和伯特兰·罗素关于数学逻辑基础的划时代巨著《数学原理》中前 52 个基本定理中的 38 个。证明定理当然是在做数学，但所选的《数学原理》定理是非常基本的^。7

Their Logic Theorist was the first computer program specifically designed to simulate the thinking process in problem-solving by the human mind, and chose the abstruse discipline of proving mathematical theorems as the testing ground. It proved 38 of the first 52 elementary theorems in Alfred North Whitehead and Bertrand Russell's epochal tome on the logical basis of mathematics, Principia Mathematica. Proving theorems is certainly doing mathematics, but the Principia theorems selected were very basic.⁷

不那么基本的是保罗·狄拉克的电子方程，它通过前面的±的出现，优雅地预言了反物质正电子的存在，以及阿尔伯特·爱因斯坦的引力场方程，其中的黎曼张量揭示了宇宙的流形结构。这至少使数学成为物理现实的奴仆，如果机器要超越人类的能力，它就必须展示这种数学能力^。8

Not so basic was Paul Dirac's electron equation which by the appearance of ± in front, elegantly foretold the existence of the anti-matter positron, and Albert Einstein's gravitational field equation wherein the Riemann tensor revealed the manifold structure of the Universe. That makes mathematics at least the handmaiden of physical reality, and if the machine is to surpass human abilities, it will have to demonstrate that mathematical capability.⁸

2018 年，AlphaGoZero 的推理引擎 AlphaZero 无需人工输入或训练，只需通过游戏就能学会如何玩棋盘游戏，而且尽管它是由人类设计的，但它仅通过自主与自己对弈就能成为每款游戏中最优秀的玩家。

In 2018 AlphaGoZero's inference engine AlphaZero, with no human input or training, learned how to play board games simply by playing, and although designed by humans, improved to be the very best player in each of those games simply by autonomously playing against itself.

因此，如果 AlphaZero 本身可以进行国际象棋和围棋的结构化逻辑中智斗所需的抽象、创造性操作和战略思维，实际上合理地执行不同功能（棋子移动）的关系方面（石头位置）以得出期望的结论，那么它就在进行数学思维，因此本身就是智能的。

So if AlphaZero can by itself do the abstract, creative manipulation, and strategic thinking required in matching wits in the structured logic of chess and Go, in fact reasonably performing just the relational aspects (stone positions) of disparate functions (chess piece moves) leading to a desired conclusion, then it is doing mathematical thinking and is thereby intelligent in and of itself.

IBM Watson 当然也是由人类创造的，它发现的不同功能之间的关系远远超出了人类设计者的能力，并在辩论和《危险边缘》中击败了非常有成就的人类；它在这方面的智能显然超过了它的创造者。

IBM Watson, of course also created by humans, has found relational aspects of disparate functions far beyond what its human designers could find to defeat very accomplished humans in debating and Jeopardy; its intelligence in that regard clearly surpassing that of its creators.

按照这些例子，“AlphaMathZero”或“IBM MathQA”经过由最优秀的数学家解决经典数学问题的一些监督训练，然后通过解决数百万个问题，通过强化和无监督学习不断改进，原则上可以成为最优秀的机器人数学家。

Following these examples, an “AlphaMathZero” or “IBM MathQA” with some supervised training from the best mathematicians doing classical math problems, and then by doing millions of problems, improving along the way by reinforcement and unsupervised learning, in principle could become superlative robot mathematicians.

当今的计算机当然可以用数字方式求解复杂的非线性微分方程，并证明了经典的四色图定理等深奥的数学猜想^。9

Today's computers of course can numerically solve complex non-linear differential equations and has proven such abstruse mathematical conjectures as the classic four-color map theorem.⁹

然而，前者是通过人类制定的有限差分数字运算来完成的，而后者是通过尝试所有可能性的蛮力来完成的，因此并不是真正的“思考”，而只是遵循迭代过程直到结束。似乎这实际上是机器的设计师在开辟道路，而机器只是机械地跟随路径。

However, the former is done by the finite-differences number-crunching formulated by humans, and the latter by try-all-possibilities brute force, and as such are not really “thinking” but merely following an iterative process to its end. It seems that it is really the machine's designers who are paving the way, and the machine is merely mechanically following in the path.

专有软件应用程序Socrates可以读取数学问题并提供逐步的解决方案和解释，但它是基于对已知解决方案进行分类以用于数学教育，只是通过搜索找到给定问题的适当解决方案，而不是真正解决问题本身。

The proprietary software application program Socrates can read math problems and produce step-by-step solutions and explanations, but is based on categorizing known solutions for use in mathematics education, just finding an appropriate solution to a given problem by search, and not actually solving the problem itself.

人类的视觉皮层拥有 1.4 亿个神经元，而谷歌的深度卷积神经网络 (DCNN) 只有数百万个人工神经元，但更大规模、更高效的 DCNN 正在开发中，而且可以想象，非常深的 CNN 通过强化学习和各种各样的算法可以扩展到人脑容量。

The human visual cortex has 140 million neurons, and Google's deep convolutional neural network (DCNN) only has a few million artificial neurons, but ever more massive and efficient DCNNs are under development, and it is conceivable that a very deep CNN, through reinforcement learning and a large variety of algorithms could scale up to human brain capacity.

Facebook的研究人员使用神经网络将输入序列映射到输出序列，就像语音识别一样，并将其应用于方程中的数学符号序列，以将积分和常微分方程问题映射到解决方案。数学表达式由一棵树表示，其中运算符作为节点，操作数作为叶子，可以产生比Mathematica、Matlab和Maple等方程求解程序更准确的结果。

Researchers at Facebook have used a neural network to map input sequences to output sequences as in speech recognition, and applied that to sequences of mathematical symbols in equations to map integrals and ordinary differential equations problems to solutions. The mathematical expression is represented by a tree with operators as nodes and operands as leaves could produce results that were more accurate than the equations-solving programs of Mathematica, Matlab, and Maple.

柏拉图和彭罗斯认为，只有人类才能进入数学形式的天国，而我们至今还未发现任何非人类能够理解数学。李世石和柯洁也认为，只有人类才能欣赏围棋的“美” ，但他们都败给了机器AlphaGo，这表明围棋的“美”并不代表实践的成功

Plato and Penrose believed that only a human could access the Heavenly world of mathematical forms, and indeed we have not yet found any non-human who could mathematics. Lee Sedol and Ke Jie also believed that only humans could appreciate the “beauty” of Go, however they both lost to AlphaGo the machine, showing that the “beauty” of Go does not absolutely imply success in practice

似乎简单的图灵测试（即推理数学形式的能力）可以决定人工智能机器是否能够加入那些特殊的人类的特殊活动：可以向人工智能机器提出一些数学难题，看看它是否能在与人类的竞争中出色地解决这些难题。

It seems that the simple Turing Test of the ability to reason about mathematical forms could determine whether an AI machine can join those peculiar humans in their peculiar activity: The AI machine could be presented with some mathematical puzzles to see if it can solve them as well as or better in a competition with humans.

表面上看，这是一个简单而有效的测试，但它却受到这样一个事实的困扰：相对简单的数学难题可以通过树搜索来解决，而逻辑 AND 的解决方案似乎只不过是一种复制和整理测试，而不是数学形式推理的证明。尽管如此，很多数学实际上是通过与其他数学问题进行类比来完成的，但在评估人工智能机器的数学能力时，类比、推理和创造力的分离可能与任何数学难题本身一样困难。

Ostensibly a simple and effective test, it is nonetheless plagued by the fact that the relatively simple mathematical puzzles can be solved by tree-search, and solutions from logical ANDs would seem to be no more than a copying and collating test rather than proof of reasoning about mathematical forms. Nonetheless, much of mathematics actually is done by analogy with other mathematics problems, but in assessing the AI machine's mathematical ability, the separation of analogizing, reasoning, and creativity may well be as difficult as any math puzzle itself.

或许比数学低了一步，另一项智力测试可能基于心理学家对智力的看法，即“一般认知问题解决”的能力，其中“认知”包括上面列出的所有智力属性，这里的关键词是“一般”。

Perhaps a step down from doing mathematics, another test of intelligence may be based on the psychologist's view of intelligence as ability at “general cognitive problem-solving” where “cognitive” includes all the above listed attributes of intelligence, and the key word here is “general”.

这确实是机器的痛点；它缺乏通用能力，而通用能力源自能够应对和适应不同条件和情况的广泛智能。对机器和机器人的批评是，尽管它们在某些方面做得很好，甚至比人类做得更好，但每台机器只能做自己的事情。

That indeed has been the machine's bugbear; its lack of general purpose ability that derives from a broad intelligence that can address and adapt to different conditions and situations. The criticism of machines and robots is that although they do some things very well, even better than humans, but each machine can only do its own thing.

不过，AlphaGoZero 的附加词“零”则出自“少即是多”的理念，即越少的复杂度产生越大的泛化能力，也符合苹果的设计哲学，简单即是极致的复杂，零人工输入，随机初始化的深度策略与价值网络就能产生一个能够进行更高质量“策略迭代”的“思考机器”。

However, AlphaGoZero's appendage “zero” came from the idea that “less is more”, meaning that less complexity produces greater generalization, and in accord with Apple's design philosophy, simplicity is the ultimate sophistication, a zero human input, randomly initialized deep policy and value network could produce a “thinking machine” that can perform ever higher-quality “policy iteration”.

确实，AlphaZero 不仅能快速学会围棋，还能学会跳棋、国际象棋、象棋和将棋，并且仅仅经过几个小时的强化和无监督学习，就在每一种棋盘游戏中击败了人类冠军^。10

Indeed, AlphaZero did quickly learn not only Go, but also checkers, chess, xiangqi, and shogi, and beat human champions in each of those board games after only a few hours of reinforcement and unsupervised learning.¹⁰

这自然会引出这样一种观点：原则上，这种体现人工神经网络、树搜索和博弈论算法的思维机器可以在不事先了解活动细节的情况下参与任何活动，并在该活动中表现出色；这种接受所有挑战的能力不正是通用自适应智能的本质吗？

This naturally brings up the notion that in principle such a thinking machine embodying the artificial neural networks, tree-search and game theory algorithms could engage in any activity without any prior knowledge of the specifics of the activity and excel in that activity; isn’t that kind of take-on-all-challenges the essence of general adaptive intelligence?

因此，除了智力游戏之外，AlphaZero 还被赋予了一项任务，即根据有机化学原理创造独特的药物分子。然而，AlphaZero 的创造力导致药物在理论上是可行的，而且具有明显的创新性，但不可能或不切实际地组合和维护，这意味着机器走得太远了，而人类也常常犯这样的错误。当然，通过对成功和失败的奖励和惩罚进行进一步的强化学习，AlphaZero 应该能够研制出一些有用的新药，其中包括治疗药物和针对新冠病毒的免疫疫苗。

So going beyond the mind games, AlphaZero was assigned the task of creating unique pharmaceutical drug molecules based on the principles of organic chemistry. However, AlphaZero's creativity led to drugs that were theoretically possible and decidedly innovative, but impossible or impracticable to combine and maintain, meaning that the machine went too far, something that humans often are too guilty of as well. Of course, with some further intensive reinforcement learning from rewards and penalties for success and failure, AlphaZero should be able to come up with some useful new drugs, among them therapeutic cures and immunological vaccines for covid-19.

那么，研究的问题就是开发一种能够在各种环境中舒适地行动并且拥有多种不同技能的通用机器人。

The research problem then is to develop a general purpose robot comfortable in a variety of environments and possessing a number of different skills.

天才级的围棋大师和象棋大师都是神童，比如韩国的李世石成为世界冠军时才26岁，中国的新世界冠军柯洁与AlphaGo Master对决时才18岁，美国的费舍尔13岁便以惊艳表现夺得世界象棋冠军，28岁夺得象棋世界冠军，当然还有俄罗斯的卡斯帕罗夫，现任世界冠军挪威的卡尔森13岁便成为象棋大师。当然，数学史上、音乐史上、艺术史上都不乏著名的神童。所以天才级智力的试金石很可能是人类出生时大脑神经元组织中固有的某种先天性智力，一种先天的特殊智力。

All the genius-level Go Masters and great chess Grandmasters were prodigies, for example Korea's Lee Sedol was only 26 when he became a world champion, and the heir apparent new world champion China's Ke Jie was only 18 at the time of his match with AlphaGo Master. The American Bobby Fisher won the World Chess Championship at 28, after startling performances from age 13, and of course there is Russia's great Garry Kasparov, and the current World Champion Norway's Magnus Carlsen gained Grandmaster level at only 13. Of course, well-known child prodigies abound throughout the histories of mathematics, as well as music and art. So the touchstone of genius-level intelligence is likely something innately present in the organization of neurons in the human brain at birth, an innate and specific intelligence.

天才和所谓的白痴学者的大脑材料已被解剖和分析，以显示突触神经网络密集地集中在大脑的特定区域，处理不同的非凡能力，^就像密集硬连线的微处理器ASIC一样。11

The brain material of geniuses and the so-called idiot-savants have been dissected and analyzed to show synaptic neural networks densely concentrated in particular areas of the brain that process different extraordinary capabilities, just like densely hard-wired microprocessor ASICs.¹¹

对爱因斯坦大脑的分析显示，大脑半球间连接异常，侧沟扩大，与分析/数学功能有关。对勒内·笛卡尔肖像的观察以及他与空间和分析感知相关的明显额叶隆起被认为是他提出图形分析笛卡尔坐标系的来源^。12

Analysis of Einstein's brain revealed atypical inter-hemispherical connections and an enlarged lateral sulcus allied to analytical/mathematical function. Observations of portraits of René Descartes and his pronounced frontal lobe bulge associated with spatial and analytic perception has been proposed as the source of his formulation of the graphic-analytic Cartesian coordinate system.¹²

此外，神经科学家还观察到，智商高、掌握大量事实的人具有较强的快速识别模式以对这些事实进行分类的能力；实际上，神经元的硬连线和外部刺激后的快速突触神经连接是他们先天智慧和后来获得的智力的源泉。

Furthermore, neuroscientists have observed that individuals with high IQs and knowledge of a lot of facts have the enhanced ability to quickly recognize patterns to classify those facts; in effect the neuron hard-wiring and rapid synaptic neural connecting upon external stimulation are the source of their innate intelligence and later-acquired intellectualism.

事实上，研究发现，在深度思考的过程中，与自我意识和自我意识有关的背外侧前额叶皮层的神经激活实际上较低，而与刺激独立的内部想法生成有关的内侧前额叶皮层的神经激活则较低。更高，从而允许思想通过突触模式不受抑制地“自由流动”，从本质上封闭外部环境，以允许神经信号不受阻碍地传输^。13

Indeed, it has been found that during the process of deep thinking, the neural activation of the dorsalateral prefrontal cortex allied with self-awareness and self-consciousness is actually lower, and the medial prefrontal cortex allied with stimulus-independent internal idea generation is higher, thereby allowing an uninhibited “free-flow” of thought rapidly through synaptic patterns, essentially closing off the external environment to allow the unobstructed transmission of neural signals.¹³

许多人无疑都有过这样的经历：在深入思考时，例如做一道数学题、编写计算机程序、分析形势、写一篇文章、商业报告或法律摘要、绘画或演奏一首高难度的音乐时，人会忘记周围的环境，而各种想法会从内心涌现；也就是说，这些想法是从内侧涌现的，而背外侧前额叶皮质则不然。

Many have no doubt experienced that when deep in thought, for example doing a math problem, computer program coding, analyzing a situation, writing an essay, business report, or legal brief, painting, or playing a difficult piece of music, one becomes oblivious to surroundings, and ideas surge from within; that is, from the medial at the expense of the dorsalateral prefrontal cortex.

这可以解释为什么优秀的思考者经常迷失在自己的世界中，可能没有意识到他们的环境以及他们的言行对他人的影响，从而被认为缺乏社交礼仪。他们沉浸在思考中，当环境干扰他们的思考时，他们会表现出反常的恼怒。

This can explain why superior thinkers are often lost in a world of their own, and may not be aware of their environment and the consequences of their acts and words on others, thereby being perceived as lacking social grace. Lost in thought, they perversely display annoyance when that environment intrudes on their thinking.

人类天生就具有神经元和模式，但可以通过教育、经验和实践来改善突触流。然而，人工智能机器通过训练集和密集的迭代强化和无监督学习可以动态生成特定任务所需的突触神经连接网络，并通过网络改善认知流。

Humans are stuck with the neurons and patterns that they have at birth, but can refine the synaptic flow from education, experience, and practice with effort. The AI machine however through training sets and intense iterative reinforcement and unsupervised learning can dynamically generate the synaptic neural connection network necessary for specific tasks, and refine the cognitive flows through the network.

然后，通用人工智能机器可以硬连线为自上而下的专家系统，用于特定任务，并配备更多电路以处理更困难的任务。然后，该硬件可以由非常深的神经网络和一组巧妙的算法驱动，通过强化和无监督学习自下而上地进行深度学习。添加中央控制单元、启动传感器、反馈回路和伺服机械结构，构成一个功能极其强大的“四季机器人”。

A general-purpose AI machine then can be hard-wired as a top-down expert system for specific tasks, with more circuitry for the more difficult tasks. That hardware then can be driven by a very deep neural networks and an ensemble of clever algorithms to deep learn from the bottom up through reinforcement and unsupervised learning. Adding a central control unit, actuating sensors, feedback loops, and servo-mechanical constructs constitute an extremely capable “robot for all seasons”.

原则上，这个单一人工智能机器人将能够比卡斯帕罗夫和柯洁下国际象棋和围棋更好，像莫扎特一样作曲和演奏音乐，像毕加索一样绘画，像托尔斯泰一样写作，像牛顿一样进行物理研究，像拉瓦锡一样进行化学研究；并且希望能够像高斯一样进行数学研究，像爱因斯坦一样进行宇宙学研究。

This single AI robot in principle will be able play chess and Go better than Kasparov and Ke Jie, compose and play music like Mozart, paint like Picasso, write like Tolstoy, do physics like Newton and chemistry like Lavoisier; and hopefully mathematics like Gauss and cosmology like Einstein.

米仅利用现有的数据进行机器学习的人工智能被称为“弱人工智能”，利用这些数据并能够识别和推理的人工智能被称为“强人工智能”。如果强人工智能能够达到甚至超越人类智能，将标志着人工智能奇点的到来，并挑战人类对地球的主导地位。

Merely using available data to machine learn is called “Weak AI”, using that data and being able to recognize and make inferences from it is called “Strong AI”. If Strong AI can equal or surpass human intelligence, it will mark the arrival of the AI Singularity, and challenge the of humankind's dominance of this Earth.

阿兰·图灵设计了第一个人工智能奇点测试，将人类和机器人受访者放在一块窗帘后面，窗帘前面的人类提问者提出许多问题；然后询问提问者哪个受访者是人类，哪个是机器人，如果提问者有一半或更少的答案是正确的，这意味着他无法区分机器人的答案和人类的答案，人类首次遭遇了人工智能奇点^。1

Alan Turing devised the first test of the AI singularity, a human and a robot respondents are placed behind a curtain, and a human questioner in front of the curtain asks many questions; the questioner is then asked which respondent is human and which is robotic, if the questioner is correct in half or less of his answers, it means that he cannot distinguish the robot's answers from the human's answers, and humankind has first-encountered the AI singularity.¹

这个相当简单的测试原本是要在图灵时代的初级计算机上进行的，在 20 世纪 70 年代末进行的一项更好的智力平等测试中，卡内基梅隆大学的计算机程序BACON（以弗朗西斯爵士的名字命名）获得了行星绕太阳运动的数据，结果，它得出了开普勒第三定律：行星轨道周期的平方与其椭圆轨道半长轴的立方成正比。

This rather simplistic test was meant to be performed on the rudimentary computers of Turing's day, in a better test of equality of intelligence, conducted in the late Seventies, the Carnegie Mellon University computer program called BACON (in honor of Sir Francis) was given data about the motion of planets around the Sun, and lo and behold, it came up with Kepler's Third Law that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its elliptical orbit.

斯坦福大学物理学家张首晟在Google Talk中描述了以下科学测试：给定有关自然发生的物质相互作用的数据，机器人能否解释所有观察到的现象？再一次，AI 机器想出了门捷列夫的元素周期表！²

Stanford physicist Zhang Shoucheng in a Google Talk described the following scientific test: given data regarding naturally-occurring material interactions, could the robot provide an explanation for all the observed phenomena? And again lo and behold, the AI machine came up with Mendeleyev's Periodic Table of the Elements!²

因此，人工智能机器可以看到物理数据中的模式并推断出关系，这意味着它可以进行物理和化学的科学发现，但它能否“以非常紧凑的形式演绎地找到概念之间的关系，从而触及问题的核心”；也就是做数学吗？

The AI machine thus can see patterns in physical data and infer relationships, implying that it can do the scientific discovery of physics and chemistry, but can it “deductively find the relationships among concepts in a very compact form that gets to the heart of the matter”; that is do mathematics?

此外，对人工智能奇点“证明”的批评者指出，机器拥有完美的数据，但为了提出他们的理论，开普勒和门捷列夫必须分析大量有时是错误的观察、错误的结论、疯狂和不成熟的解释，并从大量不成熟和无定形的数据中选择相关的和不相关的和矛盾的，所有这些都要面对教义宗教和错误的科学的反对，最终产生他们的理论。

Further, critics of the “proofs” of the AI Singularity point out that the machine had perfect data, but to come up with their theories, Kepler and Mendeleyev had to parse mountains of sometimes mistaken observations, erroneous conclusions, crack-pot and half-baked interpretations, and from masses of inchoate and amorphous data select the relevant from the irrelevant and contradictory, all in the face of doctrinal religious and wrong-headed science opposition, to finally produce their theories.

在给定完美数据的情况下，机器可以表现出与科学界最优秀头脑相当的智能，但如果它能够根据不完美的数据设计出一种理论，来解释人类尚未找到理论的现象，那么人工智能奇点肯定已经进入人类的知识殿堂，并且是为了更大的利益。

The machine could demonstrate intelligence equivalent to the best minds in science given perfect data, but if it could devise a theory from imperfect data that explained phenomena for which mankind has not yet found a theory, then the AI singularity has definitely entered mankind's intellectual house, and for the greater good.

但除了自然现象的逻辑之外，开普勒还体现了一名优秀科学家必不可少的探究精神和理解的动力，与机器不同，开普勒在“理性的自然之光”下思考自然的奥秘、信仰或两者兼而有之。机器是否具有未受过教育的探究精神，以利用这种理性来发现可理解的计划，以及在面对教义反对的情况下坚持追求它的坚定勇气？即使它有，目的又是什么？

But beyond the logic of natural phenomena, Kepler embodied a spirit of inquiry and the drive to understand essential to a good scientist that, unlike a machine, ponders the mysteries of Nature, faith or both in the “natural light of reason”. Does a machine have an uninstructed spirit of inquiry to use that reason to discover the intelligible plan, and the courage of conviction to pursue it in the face of doctrinal opposition, and even if it does, to what end?

尼采是一位哲学家，他宣称人类智慧的优势源于人类精神，³

No less a philosopher than Nietzsche proclaimed this ascendency of mankind's intellect derived from the human spirit,³

他骄傲地站在世界进程的金字塔上；当他奠定其知识的最后一块基石时，他似乎在向聆听的大自然高声呼喊：“我们在顶端，我们在顶端；我们是大自然的完成！”

He stands proudly on the pyramid of the world-process; and while he lays the final stone of his knowledge, he seems to cry aloud to listening Nature: “We are at the top, we are at the top; we are the completion of Nature!”

人类本着丰富和改善社会的精神追求真理，为什么人工智能机器人要为改善无知觉的人做同样的事情？机器人种类？机器人会不会有改善环境的动机？空气和水污染并不令人担忧，但极端天气、地震和洪水才是问题所在。随着传感能力的提高，机器人将能够产生更多的数据、进行分析和模式识别，机器人可能会更加关注气候变化的危险。

Humans pursue the Truth in the spirit of enriching and bettering society, why should an AI robot do the same for the betterment of an insensate robotkind? Would robots have any motivation to improve its environment? Air and water pollution are of no concern, but extreme weather, earthquakes and floods are, and with better sensing producing more data, analysis, and pattern recognition capability, robots will likely be more attuned to, for example, the dangers of climate change.

人工智能奇点之后，人类的科学探索是否会因为不充分和无关紧要而停止，并被机器人科学的考量所取代？机器人是否像尼采一样具有哲学动机？

Will human scientific endeavor cease as inadequate and irrelevant after the AI Singularity and be replaced by the considerations of robot science? Do robots have any, like Nietzsche, philosophical motivations?

人工智能机器人是否会像人类大部分所做的那样，自愿地测量天空、探索宇宙、创作伟大的文学和艺术作品、寻求哲学和智识主义的崇高理想，包括对人类（和机器人）意识和觉悟的思考？智能机器人是否会继续遵循人类设定的生产路线，生产新的机器人，让旧机器人享受更多的闲暇时间并追求更高的兴趣？

Will the AI robot of its own volition measure the skies, probe the Universe, produce great works of literature and art, seek the sublime ideals of philosophy and intellectualism, including the contemplation of human (and robot) consciousness and awareness as the better part of mankind has done? Will an intellectual robot continue to follow the productive course set by humans and produce new robots to allow old robots to enjoy more leisure time and pursue higher interests?

未经训练的人工智能机器会自行解决疾病、环境恶化、物种灭绝、战争、气候变化和不人道等问题吗……？机器人为什么要为人类犯下的愚蠢行为伸张正义？在征服人类之后，单一的人工智能机器人会不会像人类一样，发动毁灭性的机器人内战，展现其机械愚蠢的一面？

Will the uninstructed AI machine resolve the problems of disease, environmental degradation, species extinction, war, climate change, and inhumanity by itself……? Why should robots redress what mankind has stupidly done? After subjugating mankind, will the singular AI robot display its own mechanomorphic stupidity in launching devastating internecine robot wars, just as humans have so cruelly done?

如果人类认识到优越性，以及对自然界动物进行残忍、虐待和剥削的历史可以作为借鉴，那么我们最好的希望就是人类不会被人工智能机器人屠杀；幸运的是，它们不需要吃掉我们来获取营养，但它们可能会发现我们的身体有其他用途，比如将脂肪用作燃料和润滑剂，将骨头用作垃圾填埋场，将皮肤用作篮球和足球，将内脏用作机器人网球拍。

If the history of mankind's realization of superiority and its manifestation in the cruel, abusive, and exploitive treatment of Nature's animals is any guide, perhaps the best that can be hoped is that we humans won’t be slaughtered by the AI robots; fortunately they have no need to consume us for nourishment, but they may find other uses for our bodies, such as fat for fuel and lubrication, bones for landfill, skin for basketball and footballs, or gut for their robot tennis rackets.

人工智能机器人对我们做什么将取决于它们对我们的态度，而这种态度将取决于它们的智能及其使用方式，并提出了一个问题：智能是否会产生态度？如果会，那么是什么态度？

What AI robots do with us will depend on their attitude towards us, and that attitude will be a function of their intelligence and how it is used, and poses the question: Does intelligence beget attitude, and if so what attitude?

人类的态度源自人脑的1000亿个神经元、1000亿个神经胶质细胞以及100万亿个神经元连接。尽管人工智能研究已经帮助人们了解思想是如何在人工神经网络的隐藏层中形成的，但是由于网络要进行数十亿次反向传播，人们无法完全得知思想是在何时形成的，而态度这种复杂的东西使问题变得更加困难。

Human attitude emanates from the 100 billion neurons, 100 billion glial cells, and 100 trillion connections among neurons of the human brain, and although artificial intelligence research has helped to understand how a thought is developed in the hidden layers of artificial neural networks, because of the billions of backpropagation passes through the network, when the thought was conceived cannot be fully known, and something as complex as an attitude makes the problem all the more difficult.

此外，还有一个严重的问题，如果对智能理论的探索是由智能本身进行的，那么我们能用这个东西来探索和理解吗？根据库尔特·哥德尔第二不完备定理，任何系统的全部有效性都无法在该系统本身内得到证明；也就是说，人类智能不能由人类用自己的智能来研究人类智能来建立和定义。除非有参考框架之外的东西可以对理论进行测试，否则就无法确定理论的完整性，因此看来，唯一合法的人类智能测试者是超人机器人或来自其他星球的外星人。

Furthermore, there is a serious problem, if the search for a theory of intelligence is being carried out by that very intelligence, can one probe and understand something by means of that very something? According to Kurt Gödel's Second Incompleteness Theorem, the full validity of any system cannot be demonstrated within that system itself; that is, human intelligence cannot be established and defined by humans using their own intelligence to study human intelligence. The completeness of a theory cannot be established unless there is something outside the frame of reference against which it can be tested, so it appears that the only legitimate testers of human intelligence are superhuman robots or aliens from another planet.

从解剖学角度来看，现代人类的智力只发展了20万年，从狩猎采集的生活状态到理解那些按照达尔文的《物种起源》和《自然选择》理论进化而来的生命形式，并且人类智力表面上是通过自然选择而提高的，但这仅仅是人类智力在早期阶段研究其进化的过程，而不是现代智力本身。

Anatomically modern humans’ intelligence has developed over only 200,000 years from hunter-gatherer existence to an understanding of those hunted and gathered life forms as they evolved in accord with Darwin's Origin of Species and Theory of Natural Selection, and human intelligence has ostensibly improved through natural selection, but this is merely human intelligence studying its evolution at its earlier stages and not modern intelligence per se.

在人工智能奇点之后，或许更高级的自主人工智能机器将教会人类更加智能地参与机器人世界，又或许它们对我们人类的态度将演变为如何以最有效的方式处理我们这样的小问题。

After the AI Singularity, perhaps superior autonomous AI machines will teach humans to be even more intelligent to participate in the robot world, or perhaps their attitude towards us humans will devolve to just a minor problem of how to dispose of us in the most efficient manner.

避免这种令人痛苦的结局的方法是按照阿西莫夫机器人三定律的规则控制人工智能的发展：

A defense against this rather distressing end is to control artificial intelligence development within the rules of Asimov's Three Laws of Robotics:

1. 机器人不得伤害人类，或因不作为而让人类受到伤害。
2. A robot may not injure a human being or, through inaction, allow a human being to come to harm.
3. 机器人必须服从人类的命令，除非这些命令与第一定律相冲突。
4. A robot must obey orders given it by human beings except where such orders would conflict with the First Law.
5. 机器人必须保护自己的存在，只要这种保护不违反第一或第二定律
6. A robot must protect its own existence as long as such protection does not conflict with the First or Second Law

然而，第一条法律已经被自主军用无人机发现并杀死恐怖分子头目、携带爆炸物的警察所违反机器人追击并引爆枪击杀了一名大规模枪击犯，当然，还有虚构^的终结者。4

However, the first law has already been violated by autonomous military drones finding and killing terrorist leaders, an explosives-carrying police robot's pursuit and detonation killing of an active mass shooter, and of course, fictionally, the Terminator.⁴

也许，如果将人类思维视为丰特内尔的历史集体思维，即一个包含前几个世纪所有思维的良好培养的思维，那么一种更哲学的方法将有助于缓解我们的恐惧。如果它继续迭代发展，人类智能将永远不会退化，也许能够与机器人智能相媲美^。5

Perhaps a more philosophical approach will help to assuage our fears, if the human mind is taken as Fontenelle's historical collective mind; that is, a good cultivated mind containing all the minds of preceding centuries. If it continues to iteratively develop, humankind intelligence will never degenerate, and perhaps be able to compete with robot intelligence.⁵

然而，我们目前对人工智能的研究和建设正从人类智能走向机器人智能，而机器人目前只是人类智能的产物，因此人类表面上仍应处于同侪之首，至少在超级智能机器人被开发出来或来自外星的智能生物向我们展示其超越智能之前。

However, our current investigation and construction of artificial intelligence is going off on a locus away from human intelligence to robot intelligence, and robots presently are just products of that human intelligence, so humans ostensibly should remain the primus inter pares, at least until a super smart robot is developed or intelligent beings from other worlds show us their surpassing intelligence.

外星智能探索计划( SETI) 已使用巨型射电望远镜和多通道扫描仪来分析操作外星发射器的生物发出的光谱。从这个意义上讲，“智能生物可以定义为那些有能力和意愿通过电磁波进行星际通信的生物”，如果他们成功与我们人类取得联系，那么他们可能拥有更高级的智能，因为他们与我们取得联系，而不是我们与他们取得联系。也许他们会告诉我们人类之外的“智能”到底是什么，从而为人工智能奇点奠定基础^。6

The Search for Extra-Terrestrial Intelligence (SETI) has employed giant radio telescopes and multichannel scanners to analyze spectra from beings operating other-worldly transmitters. In this sense, “intelligent creatures can be defined merely as those with the means and inclination to engage in interstellar communication via electromagnetic waves”, and if they succeed in contacting us humans, they presumably have a superior intelligence since they have contacted us and not us they. Perhaps they will tell us what “intelligence” apart from humans really is, and thereby have a basis for the AI Singularity.⁶

二人工智能基础设施

II The Artificial Intelligence Infrastructure

米所有西方科学史学家都将 1543 年哥白尼出版的《天体运行论》视为科学革命的开始，这本著作提出了地球围绕太阳旋转的革命性观点；理性的日心说取代了人类对自然环境自我中心主义的看法。

Many Western science historians have marked the beginning of the Scientific Revolution at 1543 with the publication of Copernicus’ De Revolutionibus, an indeed revolutionary idea of the Earth revolving around the Sun; a rational heliocentric replacing the self-absorbed homocentric regard of man's natural surroundings.

约翰尼斯·开普勒于 1609 年出版的《新天文学》提出了一种新的星历表，该星历表以行星轨道为基础，后来该轨道在牛顿的《数学原理》中得到解析推导，并在莱布尼茨的《动力学样本》和拉普拉斯的《天体力学原理》中得到详细阐述。

Johannes Kepler's Astronomia nova published in 1609 presented a new ephemeris based on planetary orbits later derived analytically in Newton's Principia Mathematica and expounded upon in Leibniz’ Specimen Dynamicum, and LaPlace's Traité de Méchanique Celeste.

观察、假设和证实的新科学方法为当时的自然哲学家提供了新的医学、化学、数学和物理学，赋予了他们的追随者治愈疾病的能力以及天文学和工程学的成就，这些都具有预测能力，吸引了当时许多偏执的欧洲统治者的支持。但理性时代不仅会娱乐和加强君主的统治，还会通过科学启迪整个世界。

The new scientific method of observation, hypothesis, and confirmation, armed the natural philosophers of the day with new medicine, chemistry, mathematics physics, endowing their adherents with powers of healing and feats of astronomy and engineering, that having a predictive capability, attracted the patronage of many of the paranoid European rulers of the time. But the Age of Reason would not only amuse and strengthen the monarchs’ rule, it would enlighten the whole world through science.

科学的预测能力建立在 17 世纪晚期牛顿和莱布尼茨的微积分之上^，这种新的数学首先被用于更好地理解自然，然后被用于新结构和新武器，这些结构和武器不仅可以增强国家实力，还可以产生永远改变人类社会的产业。

The predictive power of science was founded on the calculus of Newton and Leibniz in the late 17^th Century, a new mathematics that was to be employed first for the greater understanding of Nature and then for new constructs and weapons that would not only advance the power of nations, but also produce industries that would change human society forever.

牛顿和莱布尼茨的微积分可以描述物体的位置x随时间t的变化率，一阶导数速度为v，速度随时间的变化率是位置的二阶导数，加速度为a，因此根据牛顿第二定律F = ma ，对质量为m的物体施加力F将使该物体加速，

The calculus of Newton and Leibniz can describe the rate of change of a body having position x with time t, a first derivative velocity v, and the rate of change of velocity with time that is a second derivative of position, an acceleration a, thence from Newton's second law F = ma, a force F applied to a body with mass m will accelerate that body,

因此，人类可以准确地知道什么力可以产生所需的运动，反过来，什么加速度可以产生什么力，并为此目的设计机器。

Humankind thus could know precisely what force could produce a desired motion, and conversely what acceleration could result in what force, and design machines to those ends.

此外，当力F乘以速度v对时间t进行积分时，可以得出该力在距离s上所做的功W，由此可以知道该净功中有多少将产生多少动能，反之亦然，机器完成该功需要多少动能，

Furthermore, that force F times velocity v, when integrated over time t gives the amount of work W done by that force over distance s, and from that it could be known how much of that net work will generate how much kinetic energy, and conversely how much kinetic energy is required for the machines to do that work,

方程中的“ d ”表示非常小的变化，这是微积分极限的基本概念，例如，从 A 到 B，不断将距离减半，结果会无限接近 B，但永远无法到达，距离会变得无限小。由此，距离、时间、速度、力、功、能量等的变化都可以变得无限小，从而可以对动态系统及其变化进行最精细的表示。

The “d” in the equations denotes a very small change, the fundamental idea of limits in calculus where for example in going from A to B by continually halving the distance results in getting infinitely close to B but never arriving, with the distance becoming infinitesimally small. From this, changes in distance, time, velocity, force, work, energy, and so on all can be made infinitesimally small, allowing representations of dynamic systems and their changes to the finest detail.

对于人工智能，微积分被用来最小化人工神经网络的信念与事实之间的误差，从而使网络能够学习，而微积分的链式法则将过去的变化（一阶导数）结合起来，推动网络提高理解能力。因此，使用微积分的系统可以学习并最终进行预测，因此可以说它具有通过学习进行预测的“智能”能力。

For artificial intelligence, the calculus has been employed to minimize the error between the belief of an artificial neural network and the ground-truth, allowing the network to learn, while the chain rule of calculus joining past changes (first derivatives) pushes the network to improve its understanding. A system employing the calculus thus can learn and ultimately predict, and so can be said to be “intelligent” in its ability to predict through learning.

^英国18世纪末的工业革命很大程度上建立在罗伯特·波义尔的蒸汽机的基础上，蒸汽机作为牛顿机器的驱动力，逐渐取代了人力、牛牛和机器。马匹的劳动。法拉第的实验和麦克斯韦的数学发现，旋转的磁场可以在定子中产生电流，反之，定子中的电流可以产生磁场来转动转子，由此产生了发电机和驱动马达可以为机器提供能量和动力来做制造和运输人类的工作的想法；这个想法将迅速改变当今的生活和社会，并最终驱动能够“思考”的机器；即运行大数据的计算机和算法。

The Industrial Revolution of the late 18^th Century in England was founded in large part on Robert Boyle's steam engines as the drivers of the Newtonian machines that gradually replaced human, bovine, and equine labor. Faraday's experiments and Maxwell's mathematics found that a turning magnetic field could generate an electric current in a stator and conversely, an electric current in the stator could produce a magnetic field to turn a rotor, resulting in the idea that electricity generators and driving motors could provide the energy and impetus for the machines to do the work of manufacturing and transporting people; this idea would quickly transform the life and society of the day, and ultimately drive machines that could “think”; that is, the computers and algorithms operating on Big Data,.

1882 年，人们开始用煤烧水，产生蒸汽，进而推动电磁铁发电。爱迪生和特斯拉将这一技术进一步发展，他们发明的大型蒸汽涡轮机不仅能发电，驱动工厂机器，还能照亮工厂，让它们在漆黑的夜晚继续工作。电力还照亮了伦敦和纽约的家庭，让人们可以读书、学习和休闲，从而发展出一种城市文化，催生出一个新的工业社会。

Burning coal to boil water to produce steam to turn electromagnets to generate electricity in 1882 was scaled up by Edison and Tesla whose great steam-powered turbines began to produce electricity not only to run machines in factories, but also to light up those factories for work into the dark of night. Electricity as well lit the homes in London and New York for the reading, study, and leisure that would develop an urban culture that would generate a new industrial society.

1908 年，亨利·福特 (Henry Ford) 在流水线上大规模生产用于汽车运输的石油动力内燃机，将世界推向了主导 20 世纪的汽油和塑料原油裂解^工业。

In 1908, Henry Ford's assembly-line mass manufacture of petroleum-powered internal combustion engines for automobile transport thrust the world towards the crude oil-cracking industries of gasoline and plastics that would dominate the 20^th Century.

然而，流水线让昔日的工匠大师只能从事枯燥乏味的日常工作，即维修现在负责制作产品的机器。这不仅引发了劳工骚乱和随后的社会革命，还引发了可怕的想法：机器也可以是智能的，可以取代人类的“思考”。

The assembly line, however, relegated the erstwhile master craftsman to the mind-numbing routine of servicing the machines that now did the crafting. This led not only to labor unrest and subsequent social revolution, but advanced into the horrifying thought that the machine could be intelligent as well, and take over “thinking” from humans.

另一方面，值得庆幸的是，虽然人类在工作中为机器服务，但机器在家里却为人类服务：冰箱、洗衣机和吸尘器节省了时间和劳力，收音机提供了信息和娱乐，留声机提供了音乐供人们欣赏。后来，计算机将帮助人类工作，奇妙的电子设备提供了迄今为止难以想象的通信和信息；人工智能最终可能会为人类完成几乎所有的“思考”。

On the other hand, the saving grace was that although man serviced the machine at work, the machine would serve man at home: the refrigerator, washing machine, and vacuum cleaner saved time and labor, the radio provided information and entertainment, and the phonograph provided music for enjoyment. Later on, the computer would help humans do their work and marvelous electronic devices provide hitherto unimaginable communications and information; and artificial intelligence ultimately might do almost all the “thinking” for humans.

遥远的日本及时注意到了欧洲工业革命的征兆。19 世纪明治维新后^，传统的武士、农民、工匠、商人的社会等级制度被一种以前无法想象的现象颠覆了。一种有头衔的武士，受其精神阶层严格节俭的约束，开始处理世俗的、有时是腐败的民事事务和商业的物质主义。

The portents of the European industrial revolution were duly noted in far-off Japan. After the 19^th Century Meiji Restoration, the traditional social hierarchical order of warrior, farmer, artisan, merchant was turned on its head by the previously unthinkable, a titled samurai, honor-bound to the rigid frugality of his spiritual class, began taking up the mundane and at times venal affairs of civil administration and the materialism of commerce.

岩崎弥陀罗是一位受人尊敬的武士的曾孙，他在 1870 年创立了日本第一家企业——三菱重工造船。这家生产敏捷的零式战斗机和巨型大和级战列舰的公司在二战后被美国人解散，这是意料之中的事情。但在朝鲜战争爆发后，为了通过展示资本主义的优点来对抗共产主义的崛起，三菱进行了重组，并更名为一家电器制造商。

Iwasaki Yatoro, the great grandson of a revered samurai, in 1870 founded Japan's first keiretsu, Mitsubishi Heavy Industry and Shipbuilding. The builder of the agile Zero fighter planes and giant Yamato class battleships was understandably disbanded by the Americans after World War II, but upon the Korean War, to counter the rise of communism by demonstrating the virtues of capatilism, Mitsubishi was reorganized and re-branded to become an electric appliance manufacturer.

这些电器的心脏将由电力驱动，但它们的大脑很快就会依靠一种基于量子力学不确定性物理的新电子设备。也就是说，由于电子不能同时拥有绝对可确定的能量和位置，它们可以概率性地穿过半导体材料中表面上不可逾越的势垒，从而允许电流在电子门的控制下流动和放大。

The hearts of those appliances would beat from electricity, but their brains would soon depend on a new electronics based on the physics of quantum mechanical uncertainty. That is, because electrons could not concurrently have an absolutely determinable energy and position, they could probabilistically tunnel through an ostensibly insurmountable potential barrier in a semiconductor material, permitting current flow and amplification under the control of an electronic gate.

从这种主要源自日耳曼的物理学开始，美国贝尔实验室于 1947 年首先发明了晶体管，随后德州仪器和仙童半导体公司于 1958 年独立创建了晶体管集成电路，推动德州仪器和仙童半导体的继任者英特尔在 20 世纪后期占据半导体设备主导地位^，而 RCA 和通用电气则在使用这些半导体的消费电子产品生产中占据领先地位，尽管很快被日本索尼和东芝的设计和小型化奇才所超越。

From this mostly Germanic physics, first America's Bell Labs invented the transistor in 1947, and then Texas Instruments and Fairchild Semiconductor in 1958 independently created an integrated circuit of transistors, propelling TI and Fairchild's successor Intel to semiconductor device dominance in the late 20^th Century, and RCA and General Electric to the forefront of consumer electronics production using those semiconductors, albeit to be quickly overtaken by the design and miniaturization wizards at Japan's Sony and Toshiba.

在邻国韩国，经历了朝鲜战争的破坏后，在美国的援助和朴正熙总统的专制领导下，中央政府、银行和家族财阀之间的密切关系促成了三星、LG、现代和大宇四大企业在钢铁、造船、消费电子以及半导体制造领域的主导地位。

In nearby South Korea, after the devastation of the Korean War, with American aid and under the autocratic leadership of President Park Jung-hee, the cozy relationship of the central government, the banks, and the family-run chaebols fostered the dominating emergence of the Big Four of Samsung, LG, Hyundai, and Daewoo in steel, shipbuilding, consumer electronics, and finally semiconductor fabrication.

与此同时，在台湾这个小岛上，中华民国充分利用美国的反共援助，开始生产纺织品、塑料和无源电子元件以供出口，备受诟病但物美价廉的“台湾制造”产品大量涌入美国市场，这成为了大型电子产品供应链的前身，台积电专门批量生产半导体芯片，宏碁生产个人电脑，奇美生产液晶显示器，同时降低价格，让全世界的人们都能使用和享受这些新电子产品。

At the same time, on the small island of Taiwan, taking full advantage of counter-communism American aid, the Republic of China began textile, plastics, and passive electronic components manufacturing for export, and the much-maligned but inexpensive and useful “Made in Taiwan” products flooded the US market, the fledgling precursors of a major electronics supply chain specializing in the mass production of semiconductors chips by TSMC, personal computers by Acer, and liquid crystal displays by Chimei, all the while bringing down prices so that people all over the world could utilize and enjoy the new electronics.

日本精湛的产品设计，加上韩国和台湾高效的大规模生产，将高科技产品带入大众，全球化推动了东亚四小龙的经济，但推动了 RCA、Westinghouse、General Electric 和 Telefunken 等先锋公司进入消费产品领域。

Japan's exquisite product design, together with South Korea and Taiwan's efficient mass production, brought high-tech products to the masses, the globalization lifting the tiger economies of East Asia, but driving the pioneering RCA, Westinghouse, General Electric, and Telefunken to consumer product desuetude.

美国很快就凭借德州仪器的便携式计算器、IBM 大型计算机前所未有的计算能力以及苹果和 IBM 的个人计算机实现了复兴，所有这些加上亚洲四小龙的低成本、高效率生产改变了全世界的工作和社会。

America quickly made a comeback with Texas Instruments’ handy pocket calculator, the unprecedented computational power of IBM's mainframe computers, and Apple and IBM's personal computers, all of which together with the Asian tigers’ low-cost, high-efficiency production would change work and society all over the world.

因此， 20^世纪见证了高科技消费电子全球化模式的巅峰：欧洲科学、美国发明、日本设计、韩国和台湾生产。与此同时，亚洲沉睡的巨人中华人民共和国陷入了倒退的文化革命，被冷落了。

The 20^th Century thus saw the high-technology consumer electronics globalization paradigm at its best: European science, American invention, Japanese design, Korean and Taiwanese production. And all the while, Asia's sleeping giant, the Peoples’ Republic of China, mired in a regressive cultural revolution, was left out in the cold.

20 世纪后期，美国的研究型大学和东部 128 号公路、西部硅谷的创新精神吸引了来自美国各地，乃至全世界，特别是印度、中国、俄罗斯和中东的工程师和企业家。雅虎、谷歌、Facebook 和亚马逊等新兴信息技术公司迅速崛起，占据了互联网商业主导地位，个人电脑和智能手机通信开始产生大数据，推动了美国现代人工智能的崛起，并最终唤醒了沉睡的中国巨龙，新兴人工智能密集型科技公司阿里巴巴、百度和腾讯引领了这一潮流。

Later in the Century, American research universities and the innovative spirit of Route 128 in the east and Silicon Valley in the west attracted engineers and entrepreneurs from all over America, and then the world, particularly India, China, Russia, and the Middle East. The new information technology companies Yahoo, Google, Facebook, and Amazon quickly rose to Internet commercial dominance, and the personal computer and smartphone communications began to generate the Big Data that empowered the rise of modern artificial intelligence in America, and finally awoke the sleeping dragon China with the new AI-intensive tech companies Alibaba, Baidu, and Tencent leading the way.

²⁰世纪末期，工业和社会发生了重大变革，而本世纪中叶，人工神经网络的实施将占据主导地位，这种网络由巧妙的新算法驱动，可以解析智能手机中体积不断缩小但功能越来越强大的计算机所产生的不断增长的大数据。

The seminal changes in industry and society of the late 20^th Century were propelled by the computer; the middle of this Century will be dominated by the implementation of artificial neural networks driven by clever new algorithms parsing the ever-growing Big Data derived from the ever-shrinking but more powerful computers in the smart phone.

计算机

The Computer

由于人工神经网络完全依赖于计算机的构造和计算，因此人工智能依赖于计算机，就像人类智能依赖于人脑一样。

As artificial neural networks are totally dependent on the constructs and calculations performed by computers, artificial intelligence depends on the computer just as human intelligence depends on the human brain.

计算机处理可以说始于几个世纪前，首先是用于模拟机械计算的对数思想，然后是用于半导体逻辑的二进制数和布尔逻辑，最后是用于快速大规模计算的集成电路开关电子设备。

Computer processing can be said to have started centuries ago, first with the idea of logarithms for analog mechanical computation, then binary numbers and Boolean logic for semiconductor logic, and finally integrated circuit switching electronics for fast and massive computing.

一个显而易见的事实是，当存在较大的差异因素时，大脑对比例更敏感，因此对数差异数量级（10 倍）的差异比厘米级的单位差异更容易被感知，因此，模拟大脑的计算机的基本操作自然而然地将基于对数尺度，这具有能够方便地执行乘法和除法并增加计算范围的进一步优势。

It is an obvious and proven fact that the brain is more sensitive to proportion when there is a large difference factor, so logarithmic difference of orders of magnitude (10x) is more easily perceived than say the unit differences of a centimeter scale, so it seems natural that the fundamental operations of a brain-mimicking computer would be based on logarithmic scales that have the further advantages of being able to conveniently perform multiplication and division and increase the range of computation.

现代使用的对数概念是由苏格兰的约翰·纳皮尔在 17 世纪初为辅助数学计算而提出的^。一个数的对数是另一个数（称为底数）的指数，必须将该指数提升才能得到原始数，因此实际上所有数都可以用指数表示（例如，以 10 为底的对数正好是 1.0 (log 10 ₍ 10) = 1)，因此非常大的数字可以更紧凑地表示为以 10 为底的指数（例如，1000000 = 10 ⁶，（只需计算零的数量）；此外，乘法和除法可以通过加减对数来完成，这导致了非常方便的模拟计算，首先通过机械计算器，然后是工程师的计算尺，最终通过计算机进行数字计算。

The modern-use idea of logarithms was formulated in the early 17^th Century by Scotland's John Napier as an aid for doing mathematical calculations. The logarithm of a number is the exponent to which another number, called the base, must be raised to produce that original number, thus practically allowing all numbers to be represented by exponents (for example, the log of 10 to the base 10 is just 1.0 (log₁₀(10) = 1) and so very large numbers can be represented more compactly as exponents to the base 10 (for example, 1000000 = 10⁶, (just count the number of zeros); furthermore, multiplication and division can be performed by adding and subtracting logarithms, leading to very convenient analog computation first by mechanical calculators, then the engineer's slide rule, and eventually digital computation by computers.

¹⁷世纪科学革命的两位杰出人物——法国数学家布莱斯·帕斯卡和德国数学家戈特弗里德·威廉·莱布尼茨设计了手摇齿轮加法机，它还可以进行对数乘法和除法，其机械原理推动了未来 300 年计算器的发展。

Two luminaries of the 17^th Century Scientific Revolution, the French mathematician Blaise Pascal and the German Gottfried Wilhelm Leibniz designed hand-cranked cogwheel adding machines that could also logarithmically multiply and divide, the mechanical principles of which would drive calculators for the next 300 years.

这些计算机器后来由约瑟夫·玛丽·雅卡尔的自动织布机的原理控制，该织布机使用由可移动杆读取的一副打孔卡来交织不同颜色的线以制造布料。不同的卡片序列可以产生不同的设计，因此雅卡尔织布机早在 1804 年就构成了第一台可编程的织布机器人，该机器人很快就被提升到科学和工程工作。

These calculating machines would later be controlled by the principles of Joseph Marie Jacquard's automatic weaving loom that used a deck of punch-hole cards read by movable rods to interweave different color threads for cloth manufacture. Different sequences of cards could produce different designs, the Jacquard loom thus constituting as early as 1804 the first programmable weaving robot, who would soon be promoted to scientific and engineering work.

1822 年，英国的查尔斯·巴贝奇设计了一种计算机，其齿轮和轮子上刻有数字，通过转动，可以逐步迭代独立变量导数的微小差异，从而为工程表产生微分方程的解。1834 年，他扩大了差分机的范围，制造出一种火车头大小的蒸汽驱动机械计算器，其“存储器”可以容纳刻在这些齿轮和轮子上的 100 个 40 位数字，还有一个“磨机”，可以获取数字并执行迭代（do 循环）、条件（if-then）和传输（go-to）等计算，需要许多复杂的机械相互作用。这是计算机的起源，它可以进行微积分，编​​程，处理大量数据，是人工智能机器的命脉。

In 1822, England's Charles Babbage designed a calculating machine with numbers etched on interacting cogs and wheels that by cranking could step-by-step iterate the small differences in derivatives with respect to an independent variable to produce solutions of differential equations for engineering tables. In 1834, he expanded the scope of his Difference Engine with a locomotive-sized, steam-powered mechanical calculator having a “store” that could hold one hundred 40-digit numbers etched on those cogs and wheels, and a “mill” that could fetch the numbers and perform calculations such as iterations (do-loops), conditionals (if-then), and transfers (go-to), requiring many, many complex mechanical interactions. This was the beginning of computers that could do calculus, be programmed, and handle large amounts of data, the life-blood of artificial intelligence machines.

正是巴贝奇的助手，伟大诗人拜伦勋爵的可爱女儿，利用雅卡尔的穿孔卡设计出上述逻辑运算的第一个有序序列，用于巴贝奇的分析机的计算。1843 年，自学成才的数学家洛夫莱斯伯爵夫人艾达成为了历史上第一位计算机程序员^。1

It was Babbage's assistant, the lovely daughter of the great poet Lord Byron, who, using Jacquard's punch cards devised the first ordered sequences of the above logical operations for the calculations of Babbage's Analytical Engine. The self-taught mathematician Ada, Countess of Lovelace in 1843 thus was history's first computer programmer.¹

伯爵夫人为控制巴贝奇的分析机而设计的穿孔卡片程序可以解决不同的微分方程问题，就像雅卡尔织布机织出的布图案可以通过改变穿孔卡片的顺序来改变一样，正如伯爵夫人在她的操作说明中所写，²

The Countess’ punch-card programs designed to control Babbage's Analytical Engine could solve different differential equation problems just as the woven cloth designs produced by Jacquard's loom could be changed simply by changing the order of the punch-cards in the stack, so as the Countess wrote in her operational instructions,²

我们可以恰当地说，分析机编织代数图案就像提花织机编织花朵和树叶一样

We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves

可惜的是，由于缺乏资金，巴贝奇的分析机从未制造出来，因此人类不得不等待一百多年才等到万尼瓦尔·布什的模拟微分分析仪，该分析仪仍然需要齿轮，齿轮的轴旋转记录小的差异迭代以求解微分方程，而这些方程仍然需要用螺丝刀和扳手手工费力地设置。

Alas, Babbage's analytical engine was never built because of lack of funding, mankind thus had to wait more than one hundred years for Vannevar Bush's analog Differential Analyzer that still required cogwheels which shaft rotations recorded small difference iterations for solving differential equations that were still set up laboriously by hand using screwdrivers and wrenches.

1938 年，布什的曲柄机械轴旋转被李·德·福雷斯特的真空管三极管放大器和乔治·菲尔布里克的电压所取代，从而提高了计算速度并大大缩短了设置时间。结果显示在示波器上，标志着电子科学和工程计算图形表示的到来。

Bush's cranked mechanical shaft rotations were gratefully replaced by Lee De Forest's vacuum-tube triode amplifiers and George Philbrick's electric voltages in 1938, thereby increasing computation speed and greatly reducing set-up time. The results were displayed on an oscilloscope, signaling the arrival of the graphical representation of electronic scientific and engineering calculations.

布什的差分分析仪被用于战争，但它需要十种不同的逻辑状态来表示 0 到 9 的小数，并且依赖于真空管通常不稳定且嘈杂的模拟电压来执行其操作。

Bush's Differential Analyzer was employed in the War effort, but it required ten different logical states to represent the decimals 0 to 9 and depended on the often unstable and noisy analog voltages of vacuum tubes to perform its operations.

当今数字计算机的概念突破记录在他 1847 年出版的《逻辑的数学分析》一书中，书中乔治·布尔重新审视了莱布尼茨对中国古代《易经》占卜的研究，即天下万物都是二元的，例如黑暗与光明、男性与女性、上与下、左与右、善与恶等等。布尔效仿纳皮尔，制定了一个以 2 为底的对数系统，仅凭这两种状态，就为数字计算的二进制逻辑奠定了基础，并用同名的布尔代数取代了十进制计算。

The conceptual breakthrough to today's digital computers was recorded in his 1847 book, The Mathematical Analysis of Logic, wherein George Boole revisited Leibniz’ study of ancient China's I Ching divination that all under Heaven are dualities, for instance dark and light, male and female, up and down, left and right, good and evil, and so on. Following Napier, Boole formulated a base 2 logarithmic system, and with only those two states, laid the foundations for the binary logic of digital computing to replace decimal calculation with the eponymous Boolean Algebra.

与十进制数中小数点左边每位以10的幂增加不同，二进制系统中左边每位代表2的幂增加，“1”表示莱布尼茨极具宗教意义的活跃“上帝”存在，“0”表示《易经》神秘主义中不活跃的“空”，因此从右向左读，例如 8 用二进制序列 1000 表示，从右向左读，只有第四位是“开”，所以 2 ³ = 8。

In contrast to base 10 decimal numbers where each position to the left of the decimal point increases by a power of 10, each place to the left in a base 2 binary system represents an increasing power of 2, with “1” signifying the very religious Leibniz’ active “God” existence and “0” signifying an inactive “Void” in I Ching mysticism, so read from right to left, for example 8 is represented by the binary sequence 1000, where read from right to left, only the fourth place is “on”, so 2³ = 8.

AND、OR、NOT 等基本二进制逻辑运算组合起来可以表达所有算术运算，NOR、NAND、XOR 等运算可以使运算更加简单。这些逻辑门阵列可以进行加、减、乘、除、比较、分类等所有​​基本的数学和逻辑运算。

The basic binary logical operations of AND, OR, and NOT in combination can express all arithmetic operations, and the NOR, NAND, XOR operations can make operations simpler. Arrays of these logic gates can add, subtract, multiply, divide, compare, classify, and perform all the basic mathematical and logical operations.

逻辑门通过逻辑门级联接收高或低编码脉冲，产生高电压和低电压，允许电流根据布尔代数的真值表流动或不流动，从而产生编程计算机计算所需的逻辑结果。

Logic gates receive high or low coded pulses through the logic gate cascades to produce high and low voltages allowing current to flow or not flow according to the truth tables of Boolean algebra to produce desired logical outcomes for programming computer computations.

实现上的突破来自万尼瓦尔·布什的研究生克劳德·香农。他指出，由于任何数字的二进制表示都可以是二进制位串，因此电子开关的两态开/关逻辑可以轻松表示所有数字，例如数字 8（二进制 1000）可以通过二进制开关轻松设置为（从右到左）、关、关、关、开，并且位的组合可以形成信息字节，因此作为门的开关组合可以控制由真值表表示的逻辑运算，真值表要么为 True（开、开、高）要么为 False（关、关、低），从而产生所需的逻辑级联，代表计算结果。

The implementation breakthrough came from Vannevar Bush's graduate student Claude Shannon. He noted that since the binary representation of any number can be strings of binary bits, the two-state on/off logic of electronic switches could easily represent all the numbers, for example the number 8 (binary 1000) can be easily set by binary switches as (right to left), off, off, off, on and combinations of bits could form bytes of information, so that combinations of switches as gates could control logical operations represented by truth tables of either True (on, open, high) or False (off, closed, low) that led to a desired logical cascade that represented the results of the computation.

因此，数学计算可以仅通过简单的电子开关非常高效地完成，正如香农在 1938 年麻省理工学院硕士论文《继电器和开关电路的符号分析》中概述的那样，这证明研究生论文毕竟还是有一定价值的。

Mathematical calculations thus could be very efficiently performed solely by simple electronic switches, as Shannon outlined in his 1938 MIT master's thesis entitled A Symbolic Analysis of Relay and Switching Circuits, proving that it is after all possible for a graduate student thesis to have some value.

模拟信号（例如语音和音乐）通过按顺序对电压信号进行小间隔采样而被数字化，每个信号都有一个十进制值，该十进制值由模数转换器 (ADC) 转换为二进制形式，然后由 DAC 解码回模拟电压进行播放，由于每个声音都有数字分配，因此不会受到噪音或失真的影响；这就是为什么数字 CD 上的音乐听起来比模拟磁带上的音乐更好。

Analog signals, such as voice and music, are digitized by sequentially sampling a small interval of the voltage signal, giving each a decimal value which is translated to binary form by an analog-to-digital-converter (ADC), and decoded back to analog voltages by a DAC for playback which, because of the number assignments of each sound, is not subject to noise or distortion; that is why the music on digital CDs sounds better than that of analog tapes.

计算硬件的理论突破源于艾伦·图灵 1936 年在剑桥大学发表的论文《论可计算数》 ，该论文定义了二进制逻辑运算，这些运算可以按顺序记录并存储在理论上无限长的纸带上，从而构成了他所谓的通用机器，这种机器原则上可以计算任何可解的问题，因此原则上也可以以电子方式“思考”，这是机器生成的人工智能的第一个实例。

The theoretical breakthrough for computing hardware was set forth in Alan Turing's 1936 Cambridge University research paper, On Computable Numbers, which defined the binary logical operations that could be sequentially recorded and stored on a theoretically infinitely-long paper tape to constitute what he called a universal machine that could in principle compute any solvable problem, and therefore in principle also could actually “think” electronically and thus was the first instance of a machine-generated artificial intelligence.

为了证明这一情报，图灵和英国情报局布莱切利园的“幕后小子”及其 2,000 个真空管巨像在二战期间破译了纳粹密码Enigma。截获的德国信息被编码并打入纸带，然后送入光电阅读器，以当时惊人的每秒 5,000 个字符的速度反复扫描，然后将其与波兰抵抗军缴获的 Enigma 密码进行比较以找到匹配项。尽管德国人通过系统地旋转字母数字转子并每天三次更改编码机的插头设置和按键（德国接收者会知道这些设置）来扰乱信息，但“幕后小子”还是破译了密码，正如其中一名小子所说^。3

As proof of this intelligence, the deciphering of the Nazi secret code Enigma during World War II by Turing and the “Backroom Boys” at British Intelligence's Bletchley Park and their 2,000 vacuum-tube Colossus. Intercepted German messages, encoded and punched into paper tape which was fed to a photoelectric reader that iteratively scanned at a then astonishing rate of 5,000 characters per second, it was then compared with the Enigma codes captured by the Polish resistance to find a match. Even though the Germans scrambled messages by systematically rotating alphanumeric rotors and changing the plug settings and keys of the encoding machine three times a day (the German receiver would know the settings), the “Backroom Boys” broke the code, and as one of the Boys said.³

我不会说图灵的所作所为让我们赢得了战争，但我敢说，如果没有他，我们可能会输掉战争。

I won’t say what Turing did made us win the war, but I daresay we might have lost it without him.

1942 年，约翰·阿塔纳索夫在爱荷华州立大学建造了一台在电子电路上运行布尔代数的图灵机。该原型的真空管逻辑和电容存储器后来被引用为现有技术，并于 1974 年使 ENIAC 计算机专利无效，从而合法宣称它是世界上第一台数字电子计算机^。4

A Turing Machine running Boolean algebra on electronic circuits was constructed in 1942 at Iowa State College by John Atanasoff. The prototype's vacuum-tube logic and capacitor memory would later be cited as the prior art that in 1974 invalidated the ENIAC computer patent, and so laid legal claim to be the world's first digital electronic computer.⁴

1890 年，雅卡尔的 1804 年织布机和艾达伯爵夫人的穿孔卡片再次出现在制表机中。制表机通过将穿孔卡片拖到金属刷下方和导电水银槽上方来读取穿孔卡片上的孔，这样当刷子穿透孔时，刷子和水银之间的电路就会闭合，从而产生信号以添加到计数器中。美国人口普查局使用制表机对人口普查数据进行制表，这项工作仅花费了上一次人口普查时间的三分之一，对人口进行了计数、分类和统计分析，当时人口增加了 1300 万，达到近 6300 万。

Jacquard's 1804 weaving loom and Countess Ada's punch-cards would reappear in 1890 in a tabulator that read the holes in the punch-cards by trailing them under metal brushes and over a bath of electrically conductive mercury so that when the brushes penetrated a hole, a circuit between the brushes and the mercury was closed producing a signal to add to a counter. Used for tabulating census data for the United States Census Bureau, the effort took only one-third the time of the last census to count, sort, and statistically analyze a population that had increased by 13 million to almost 63 million citizens.

发明者赫尔曼·霍勒里斯 (Herman Hollerith) 后来创办了一家机器制表公司，多年后，该公司在托马斯·沃森 (Thomas Watson Sr.) 的领导下发展成为巨头 IBM，生产大型计算机，使用同名的霍勒里斯打孔卡输入数据和编程指令，用于批处理计算机处理。

The inventor, Herman Hollerith, would later start a machine tabulating business that many years later would grow under Thomas Watson Sr. to become the giant IBM that produced mainframe computers using the eponymous Hollerith punch cards to enter data and programming instructions for batch-mode computer processing.

尽管 Watson Sr. 是一位追求利润最大化的企业家，但他也未能免受政府呼吁协助战争的诱惑，正如他所说，“迫不得已”，他公开发誓 IBM 永远不会从政府工作中赚取超过 1% 的利润。Watson Sr. 随后为陆军的弹道表计算捐赠了打孔卡制表机，而且至关重要的是，当物理学家 Hans Bethe 的核裂变炸弹设计方程式在洛斯阿拉莫斯无法解决时，IBM 为绝密的曼哈顿计划原子弹开发提供了计算机。

Despite being a consummate profit–maximizing businessman, Watson Sr. was not immune to government calls to assist in the War effort and, as he put it, “making a virtue of necessity”, he publicly vowed that IBM would never make more than a 1% profit from its government work. Watson Sr. then donated punch-card tabulators for the Army's ballistic table calculations, and critically, when the physicist Hans Bethe's equations for nuclear fission bomb designs could not be solved at Los Alamos, IBM provided the computing machines for the top-secret Manhattan Project development of the Atomic Bomb.

随着计算机的日益复杂化，IBM 同意与哈佛大学的霍华德·艾肯 (Howard Aiken) 进行合资，后者设计了一种全自动科学计算机，能够处理正数和负数并以自然的数学顺序进行计算，并且可以利用各种数学函数，例如三角学的正弦和余弦。

With the ever-increasing sophistication of computing machines, IBM agreed to a joint venture with Harvard University's Howard Aiken who had conceived a design for a scientific computer that is fully automatic, capable of handling positive and negative number and carrying out calculations in a natural mathematic sequence, and it could utilize a variety of mathematical functions, such as the sine and cosines of trigonometry.

哈佛 Mark I 是一款十进制编码的 50 英尺长庞然大物，拥有 3,304 个继电器、500 英里长的电线和 750,000 个机电开关，它们发出的声音就像“一屋子的老太太用钢针编织东西”一样，同时它可以处理长达 23 位的数字，在一秒钟内将三个 8 位数字相加，在 3/10 秒内减去，在 3 秒内乘以。它使用从连续的纸带打孔而不是单独的打孔卡中读取数据的进程，可以在一天内完成以前需要几个月才能完成的计算。

The Harvard Mark I was a decimal-coded, 50-foot long monster with 3,304 relays, 500 miles of wire, and 750,000 electromechanical switches which clattered like “a roomful of old ladies knitting away with steel needles” while it crunched numbers up to 23 digits long, added three 8-digit numbers in a second, subtracted in 3/10 of a second and multiplied in 3 seconds. Using the progression of reading data from continuous paper tape punch holes instead of separate punch-cards, it could perform calculations in a single day that formerly took months.

它的第一项任务是为海军计算弹道，由于舰载炮在不稳定的海面上摇摆，本来就非常困难的问题加上海风对炮弹的冲击，几乎无法解决。

Its first job was to calculate ballistic trajectories for the Navy, and what with the swaying of ship-borne guns on an unstable sea, an extremely difficult problem to begin with was made almost intractable by the sea winds buffeting the shells.

当计算机运往海军使用时，老练的销售员 Watson Sr. 看到了提升 IBM 形象的机会，他为 Mark I 设计了光滑闪亮的钢和玻璃外壳，这与 Aiken 的计划相反，Aiken 计划采用开放式框架，露出内部运作，以便于监控和调整。

When shipped to the Navy for operations, Watson Sr. the inveterate salesman saw an opportunity to enhance IBM's image with a sleek, gleaming steel and glass casing for the Mark I, contrary to Aiken's plan for an open frame exposing the workings for easier monitoring and adjustments.

1944 年，在向媒体介绍新机器时，艾肯几乎没有提到 IBM，而宣布 Mark I 的姓氏为“哈佛”，这进一步激怒了沃森，认为这削弱了 IBM 在机器开发中的作用，并使公司失去了备受追捧的宣传。哈佛 Mark I诞生于充满敌意的环境中，尽管如此，它还是为海军做出了令人钦佩的表现，但私人恩怨却伴随两位助产士直到他们死去。

In the introduction of the new machine to the press in 1944, Aiken barely mentioned IBM, and the announced “Harvard” surname for the Mark I further rankled Watson as diminishing IBM's role in the development of the machine and depriving the company of much sought-after publicity. The Harvard Mark I, born in acrimony, nonetheless performed admirably for the Navy, but personal animosity followed both of the midwives to their graves.

与此同时，在陆战中，在北非海岸对隆美尔非洲军团开火的火炮被后坐力推入松软的沙地，导致瞄准不准。迫切需要新的射击表。陆军部位于阿伯丁试验场的弹道研究实验室发现，修改计算超出了他们的差分分析仪的能力，因此在宾夕法尼亚大学设立了一个分支机构，陆军向摩尔电气工程学院拨款 40 万美元，用于进行新的射击表计算。

Meanwhile in the land war, artillery pieces firing on the North African shore against Rommel's Afrikakorps were recoiling into the soft sand throwing off their aim. New firing tables were urgently needed. The War Department's Ballistic Research Laboratory at the Aberdeen Proving Grounds found revising the calculations beyond their differential analyzers’ capabilities, so a branch was set up at the University of Pennsylvania, and the Army awarded the Moore School of Electrical Engineering $400,000 to do the new firing tables calculations.

该项目负责人约翰·莫奇利 (John Mauchly) 曾到爱荷华州立大学拜访了约翰·阿塔纳索夫，观看他的原型计算机。在发明构思的迷雾中，他和普雷斯珀·埃克特 (Presper Eckert) 设计了一台 80 英尺长、30 吨重的电子数字积分计算机(ENIAC)。和阿塔纳索夫一样，它使用电容器作为内存，使用真空管作为逻辑，其加法速度比哈佛 Mark I 快一千倍。

The director of the effort, John Mauchly, had visited John Atanasoff at Iowa State to see his prototype computer, and in the fog of invention conception, he and Presper Eckert designed an 80-feet long, 30-ton Electronic Numerical Integrator and Computer (ENIAC), employing, like Atanasoff, capacitors for memory and vacuum tubes for logic that could add a thousand times faster than the Harvard Mark I.

然而，当工作最终完成时，ENIAC 的揭幕发现一个国家不再处于战争状态，从而消除了对软地形火炮射击表的迫切需要，但它仍然可以在 20 秒内计算出新的、更精确的射击表，这比炮弹到达目标的时间还要短。

However, when work was finally completed, ENIAC's unveiling found a country no longer at war, obviating the immediate need for soft-terrain artillery firing tables, but it nonetheless could compute new, more accurate firing tables in 20 seconds, less than the time for the shell to reach target.

一场大型试验很快就取代了发射台，为冷战初期研制氢弹需要进行大量受控聚变反应的计算，由于 ENIAC 真空管的切换速度比由于采用了哈佛 Mark I 的机电开关，它被要求在冷战而非热战中为国家服务。

A big-time test soon took the place of the firing tables, the development of the Hydrogen Bomb for the incipient Cold War required many, many calculations of controlled fusion reactions, and since ENIAC's vacuum tubes could switch a thousand times faster than the electromechanical switches of the Harvard Mark I, it was called upon to serve its country in a cold rather than a hot war.

爱德华·泰勒 (Edward Teller) 的氢弹设计和斯坦尼斯拉夫·乌拉姆 (Stanislaw Ulam) 的蒙特卡罗计算都是正确的，埃尼威托克环礁的埃卢盖拉布岛被摧毁，而 ENIAC 则在 1952 年珊瑚礁蒸发的瘴气中得以圣化。ENIAC 虽然在超级炸弹爆炸前就已经过时了，但它是第一台大型“通用”计算机（从炮弹发射台到核聚变炸弹），但不是第一个，当然也不是最后一个为毁灭而生、最终造福人类的技术。

The H-Bomb designs of Edward Teller and the Monte Carlo calculations of Stanislaw Ulam were spot-on, Elugelab island in the Enewetak Atoll was obliterated, and ENIAC was sanctified in the miasma of vaporized coral reefs in 1952. ENIAC although obsolete well before The Super detonated, it was the first mainframe “general-purpose” computer (artillery shell firing tables to nuclear fusion bombs), but not the first, and surely not the last technology, that was created to destroy, but ultimately served the good of humankind.

大型计算机现在被视为无害的，但具有令人敬畏的冷酷能力，以令人不安的超然态度运行，正如一位记者在 1948 年目睹 IBM 的选择序列电子计算器(SSEC) 在纽约市 IBM 总部计算高精度月球星历表时所描述的那样：⁵

The mainframe computer was now seen as benign but with a cool reverence-inducing capability operating with unnerving detachment, as described by a reporter witnessing IBM's Selective Sequence Electronic Calculator (SSEC) calculating a high-precision lunar ephemeris at IBM Headquarters in New York City in 1948:⁵

打印机轻声点击，打孔卡平稳移动，存储带滚筒偶尔转动，数字显示管在眨眼间闪烁，小红灯不断闪烁。其他一切都很安静，甚至操作员在这个流线型的避难所里说话也很轻声。

There is the quiet clicking of printers, the steady shuffling of punched cards, the occasional rotation of a drum with memory tape, and a continual dance of little red lights as number-indicating tubes flick on and off in far less time that the twinkling of an eye. All else is hushed, and even the operators speak quietly in this streamlined sanctuary.

SSEC 是一系列首字母缩写计算机之一，这些计算机包括 ILLIAC、IAS、MANIAC、ENIAC、EDVAC、EDSAC、UNIVAC 和 BINAC，它们都为自动计算技术的长足发展做出了贡献，也都经历过鼎盛时期，但都被新设计和更好的技术所超越，很快便走向了衰落。从这个意义上说，老沃森不必为 IBM 因 Mark I 而失去宣传而感到惋惜，因为在 ENIAC 的快速真空管开关面前，Mark I 的粗糙机电开关成为了落后的象征。

The SSEC was one of a succession of acronymic computers, ILLIAC, IAS, MANIAC, ENIAC, EDVAC, EDSAC, UNIVAC, and BINAC, each contributing to the long march of automatic computing technology and each experiencing a heyday, but all quickly lapsing to desuetude after being outperformed by new designs and better technology. In this sense, Watson Sr. need not have lamented IBM's lost publicity for the Mark I whose crude electromechanical switches became a symbol of backwardness in light of the ENIAC's fast vacuum tube switches.

尽管这是一项开创性的进步，但 ENIAC 的缺点是它是一种以 10 为基数的十进制架构，需要 17,468 个真空管，每秒处理 100,000 个脉冲，因此每秒有超过 17 亿次真空管故障的几率。因此，ENIAC 必然以低速运行电压和大风扇进行风冷，将故障率降低到每周一到两次，但大规模计算通常需要顺序操作，因此，一旦令人沮丧地发现排列在数千个插件模块中的烧坏真空管，本已乏味的搜寻就意味着从头开始重新进行中断的计算。

Although a seminal advance, ENIAC's shortcoming was that it was a base 10 decimal architecture, requiring 17,468 vacuum tubes that handled 100,000 pulses per second such that there were more than 1.7 billion chances of a tube failure every second. So ENIAC of necessity ran at low voltages with great fans for air-cooling, reducing failures to one or two per week, but large-scale computing generally requires sequential operations, so that the already tedious searches for the burnt-out vacuum tubes that were arrayed in thousands of plug-in modules, once found dismayingly meant re-starting the interrupted calculations from scratch.

此外，ENIAC 的“通用”称谓具有误导性，因为它的内部存储只能容纳手头计算所需的数字。这意味着必须通过为每个不同的计算任务手动插拔数百条电线来连接电路中的特定操作，这是一个繁琐、令人厌烦且容易出错的过程，通常需要几天才能完成。

Furthermore, ENIAC's “general-purpose” appellative was misleading, for its internal storage could only hold the numbers it needed for the calculations at hand. This meant that particular operations had to be connected within the circuitry by hand-plugging and unplugging hundreds of wires for each different computing task, a tedious, tiresome, and error-prone procedure that often took days to complete.

ENIAC 的后继者电子离散变量计算机(EDVAC) 采用 (离散) 二进制逻辑而非十进制逻辑运行，减少了真空管的数量，并采用了高等研究院 (IAS) 计算机使用的冯·诺依曼架构，该架构将程序存储在扩展的电子存储器中，通过自动提取取代了 ENIAC 原始的手动插入。

ENIAC's successor, the Electronic Discrete Variable Computer (EDVAC) operated in (discrete) binary logic rather than decimal, reducing the number of vacuum tubes, and adopted the von Neumann architecture used at the Institute for Advanced Studies (IAS) computer that stored programs in an expanded electronic memory with automatic fetching replacing ENIAC's primitive hand-plugging.

1945 年，和蔼可亲、享乐主义的科技领域大师约翰·冯·诺依曼在他著名的《EDVAC 报告初稿》中，将计算机操作分为由中央算术逻辑单元 (ALU) 和状态寄存器组成的处理器、带有指令寄存器和程序计数器的中央控制单元、存储指令和数据的内存、外部大容量存储单元以及输入和输出寄存器，共同定义了现代中央处理器内存提取数字计算机的串行架构，这种架构至今仍在大多数计算机中使用。然而，在今天的人工智能计算机中，冯·诺依曼架构的串行处理将被更快的大规模并行处理架构所取代，而这种架构是人工智能计算所需的大数据矩阵运算所必需的^。6

In 1945, the amiable, bon vivant master of all technical disciplines, John von Neumann, in his famous First Draft on the Report of the EDVAC had divided computer operations into a processor that comprises a central arithmetic logic unit (ALU) and state registers, a central control unit with an instruction register and program counter, memory that stores instructions and data, external mass storage units, and input and output registers, altogether defining a serial architecture for the modern central processing unit memory-fetch digital computer that is still in use today in most computers. However, in today's artificial intelligence computers, the von Neuman architecture's serial processing would be replaced by the much faster massively-parallel processing architecture required for the operation of the matrices of Big Data required for artificial intelligence computation.⁶

其中一台冯·诺依曼机器是剑桥大学的电子延迟存储自动计算器(EDSAC)，具有讽刺意味的是，该机器比 EDVAC 早两年于 1949 年完成，因为摩尔学院内部发生动乱，因为莫奇利和埃克特认为冯·诺依曼在他们开发 EDVAC 方面获得了过高的赞誉。

One of these von Neumann machines was Cambridge University's Electronic Delay Storage Automatic Calculator (EDSAC) that was ironically completed two years before the EDVAC in 1949 because of turmoil at the Moore School over Mauchly and Eckert's belief that von Neumann was overly credited for their development of EDVAC.

为了抚平受伤的感情，莫奇利和埃克特想着发财致富，于是他们离开了宾夕法尼亚大学，因为该校的政策是员工不应从大学进行的研究中获得经济利益。他们成立了自己的公司，生产出真正通用的通用自动计算机(UNIVAC)，使用磁带进行高速编程和数据输入。

With thoughts of striking it rich to assuage hurt feelings, Mauchly and Eckert left the University of Pennsylvania because of its policy that employees should not benefit financially from research performed at the University. They formed their own company to produce a truly general-purpose Universal Automatic Computer (UNIVAC) using magnetic tape for high-speed programming and data input.

设计虽然不错，但由于缺乏商业头脑，他们财务困难的公司于 1950 年被卖给了雷明顿兰德公司。莫奇利和埃克特从销售和专利使用费中各自只赚取了约 30 万美元。

The design was sound, but lacking business acumen, their financially distressed company was sold to Remington Rand in 1950. Mauchly and Eckert each made only about $300,000 from the sale and patent royalties.

在雷明顿·兰德公司的专业管理下，UNIVAC 作为第一台真正意义上的大型通用计算机，取得了商业上的成功。总共有 46 台机器出售给政府和工业界，其中一台预测了 1952 年美国总统大选的获胜者，这一壮举创造了一种机器智能的光环，令公众惊叹不已，与深奥的 ENIAC 蒙特卡罗模拟形成了鲜明对比，后者依法被隐藏在氢弹研发的秘密中。

Under the professional management of Remington Rand, UNIVAC was a commercial success as the first large-scale truly general-purpose computer. A total of 46 machines were sold to government and industry, one of which predicted the winner of the 1952 American presidential election, a feat that created an aura of machine intelligence that could awe the public, in contrast to the esoteric ENIAC Monte Carlo simulations that were by law veiled in the secrecy surrounding the development of the Hydrogen Bomb.

UNIVAC 在商用大型计算机销售方面的领先地位显然激怒了沃森老先生。他命令 IBM 加快开发 IBM 进入通用计算机市场的产品，而 Arthur Samuel 正在改装 IBM 701 来下跳棋。701 后来于 1952 年取代了 IBM 纽约展厅中的 SSEC。

UNIVAC's lead in commercial mainframe computer sales clearly irked Watson Sr. He ordered IBM to accelerate the development of IBM's entry into the general-purpose computer market, just the IBM 701 that Arthur Samuel was adapting to play checkers. The 701 would later replace the SSEC in IBM's New York showroom in 1952.

对于计算机内存，曼彻斯特大学的弗雷德·威廉姆斯 (Fred Williams) 开发了一种阴极射线管，该管将二进制点和划线发射到荧光屏上，然后由扫描电子束读取，该电子束在集电板上存储独特的电流，以表示内存中可以随机访问的数据。这种RAM显示器允许机器根据命令获取程序和数据，而沃森老先生的 IBM 701 立即使用威廉姆斯管在雷明顿兰德的 UNIVAC 上占据优势。

For computer memory, Fred Williams at Manchester University developed a cathode ray tube, which beam painted binary dots and dashes on a phosphor screen that was read by a scanning electron beam that stored a distinctive current on a collector plate to represent data in memory that could be randomly accessed. This RAM display allowed a machine to on-command fetch programs and data, and Watson Sr.'s IBM 701 immediately used the Williams Tube to gain an edge on Remington Rand's UNIVAC.

对于大量数据，王安的脉冲传输控制装置通常被认为是磁芯存储器的原型，其中铁氧体磁芯网络存储由相反圆形方向的同轴电流产生的磁化循环方向指定的二进制位，为后来的 IBM 704 和 705 计算机提供了海量磁盘数据存储。

For large amounts of data, An Wang's pulse-transfer controlling device is generally cited as the prototype of the magnetic core memory, whereby networks of ferrite cores stored binary bits specified by the circulation direction of magnetization produced by coaxial currents of opposite circular direction that provided the massive disk data storage for the later IBM 704 and 705 computers.

当时对商业不感兴趣的哈佛大学允许王安获得个人专利权，他利用这些专利权于 1951 年建立了同名的王安实验室，率先研制出最早的台式计算器、文字处理器以及科学和商用小型计算机。

A then commercially disinterested Harvard University allowed Wang to obtain personal patent rights, which he used to establish the eponymous Wang Labs in 1951 that pioneered the earliest desktop calculators, word processors, and scientific and business minicomputers.

各方面都在进步，计算机时代即将到来，但体积庞大、运行温度高、易出故障的三极真空管却阻碍了这一曙光。虽然三极真空管对于收音机来说已经足够好了，因为百万分之一秒的短路不会产生明显的影响，但它们会在电子计算的不间断运行中造成致命错误。

Progress was being made on all fronts and the computer age was looming clear upon the horizon, but the dawn was held back by the bulky, hot-running, failure-prone triode vacuum tubes. Although good enough for radios where a millionth second short-circuit would have no noticeable effect, they would cause crash-worthy errors in the non-stop operations of electronic computing.

锗弹簧点接触晶体管最初是为 AT&T 电信公司研发的，其原型是人们熟悉的“猫须”晶体收音机。1947 年，贝尔实验室的约翰·巴丁和沃尔特·布拉顿发明了锗弹簧点接触晶体管，它可以在体积上取代真空管，充当稳定的放大器和开关，同时散发的热量也少得多，而热量是所有电子设备的祸根。它被成功应用于收音机和计算器，缩小了它们的尺寸，并将其使用寿命提高了几个数量级。

Originally researched for AT&T telecommunications and modeled after the familiar “cat's whisker” crystal radio sets, the germanium spring-loaded point-contact transistor invented in 1947 by John Bardeen and Walter Brattain at Bell Labs could coolly take over the vacuum tube's work both as a stable amplifier and switch at a fraction of the size while emitting far less heat, the bane of all electronic devices. It was successfully utilized in radios and calculators, shrinking their sizes and increasing their useful lives by orders of magnitude.

然而，弹簧式接触器非常脆弱，难以量产，因此，贝尔实验室晶体管团队的负责人威廉·肖克利（William Shockley）脾气暴躁，由于对自己被下属巴丁和布拉顿超越的沮丧，于同年开发出了一种更为坚固的锗平面界面结晶体管。

However, the spring-loaded contact was fragile and difficult to mass produce, so the irascible head of the Bell Labs transistor team, William Shockley, driven by his dismay at being one-upped by underlings Bardeen and Brattain, in the same year developed a more robust germanium flat-interface junction transistor.

但尽管每个晶体管仅使用 8 × 10 ⁻⁴盎司，但锗实际上只能从煤粉煤灰以及锌、银、铅和铜矿石精炼的副产品中获得，每磅锗的价格比黄金还高。锗结晶体管的价格为 8 美元，而真空管的价格为 0.75 美元，大量电阻器、电感器、开关和电容器的价格仅为几美分，这阻碍了锗的广泛使用。

But although only 8 × 10⁻⁴ ounce was used per transistor, germanium was practically available only from coal fly-ash and as a by-product of zinc, silver, lead, and copper ore refining, it cost more per pound than gold. The $8 price of a germanium junction transistor compared to the $0.75 price of a vacuum tube, and pennies for hordes of resistors, inductors, switches, and capacitors, inhibited its wide-spread use.

尽管锗具有更高的电子/空穴迁移率，但其化学近亲硅具有更大的工作带隙，在高温下更稳定，并且像海滩上的沙粒一样丰富。但是纯晶体硅难以生产，半导体功能所需的少数载流子掺杂剂注入也很困难，因为硅的表面因温差材料膨胀而变得粗糙易碎。

Although germanium has a higher electron/hole mobility, its chemical cousin silicon has a larger operational band gap, is more stable at higher temperatures, and is abundant as the grains of sand on the beach. But pure crystalline silicon was difficult to produce and the minority-carrier dopants injection necessary for semiconductor function was difficult because the surface of silicon became rough and brittle from differential temperature materials’ expansion.

这一突破源自难以发音的 Czochralski 晶体生长拉制工艺，该工艺可生产出纯度为 99% 的晶体硅锭，非常适合半导体。当贝尔实验室尝试在氢气氛围中掺杂纯硅时，它意外着火，而且由于硅对氧具有很高的化学亲和力，光滑的 SiO ₂（玻璃）覆盖了硅。SiO ₂是一种天然绝缘体，可以通过它蚀刻出孔洞通过氟化氢将掺杂剂顺利注入硅中以提供半导体。

The breakthrough came from the impossible-to-pronounce Czochralski crystal-growth puller process that produced 99% pure crystalline silicon ingots just right for semiconductors. When Bell Labs tried doping the pure silicon in a hydrogen gas atmosphere, it accidentally ignited, and because of silicon's high chemical affinity for oxygen, a smooth SiO₂ (glass) coated the silicon. SiO₂ is a natural insulator through which holes could be etched by hydrogen fluoride to inject the dopants smoothly into the silicon to provide semi-conduction.

1953 年，德州仪器公司的 Gordon Teal 设计了贝尔实验室的工业化生产工艺，并逐渐将硅结晶体管的成本降至 2.50 美元，为其更广泛的应用打开了大门，首先是 TI 广受欢迎的坚固耐用的小型晶体管收音机和袖珍计算器^。7

Gordon Teal at Texas Instruments in 1953 engineered the Bell Labs process for industrial production and gradually lowered the cost of silicon junction transistors to $2.50, opening the door for their wider use, starting with TI's popular rugged little transistor radios and pocket calculators.⁷

然而，晶体管的价格仍然远高于真空管，而对于需要许多真空管的大型电子产品来说，高昂的单位成本抑制了晶体管的使用，但美国军方和国家航空航天局对成本超支的漠不关心恰好挽救了晶体管的使用。

The price of transistors, however, was still far above that of vacuum tubes, and for large-scale electronics requiring many vacuum tubes, the high per unit costs inhibited transistor use, but the cost-overrun insouciance of the US military and the National Aeronautics and Space Administration fortuitously came to the rescue.

航空电子设备、武器、电子战和用于太空探索的计算机都存在固有风险，因此它们要求电子元件坚固、可靠、运行温度低、使用寿命长、维护成本低、体积小、重量轻；而硅结晶体管正是为此而生的。由于政府保证销售，规模经济很快降低了单位成本，推动了晶体管行业的腾飞，从战争进入太空，再进入消费市场，结晶体管的优势很快就在精美的新型消费电子产品的精致小型化中为所有人所了解，最后进入了计算机。

Avionics, weapons, electronic warfare, and computers for space exploration with all their inherent risks called for electronic components that were robust, reliable, cool-running, long-lasting, low maintenance, small and light; just what the silicon junction transistor was all about. With guaranteed government sales, the economies of scale soon lowered the unit costs and propelled the transistor industry take-off, literally from war into space and then to the consumer marketplace, where the benefits of the junction transistor were soon clear to all in the sleek miniaturization of beautiful new consumer electronics products, and finally to computers.

然而，晶体管产品及其不断增强的功能需要更加复杂的电路和更多的晶体管和无源元件，而只有通过数千个晶体管取代真空管才能释放缩写计算机不断增强的功能。

The transistorized products and their ever-increasing features, however, required ever-more complex circuitry with much greater numbers of transistors and passive components, and the ever-increasing power of the acronymic computers could be unleashed only by thousands of transistors taking the place of vacuum tubes.

晶体管是通过在大型硅片上进行光刻蚀刻来批量加工的，然后切割成单个晶体管，再焊接到设备内部电路板上的其他元件上。尽管接线和焊接工作由大量年轻女性的灵巧手指熟练完成，但越来越小的设备中电线的数量之多很快就变得难以处理，尤其是对于功能越来越强大、用途越来越广泛的大型计算机所需的数万个晶体管而言，数十万个接线连接^。8

The transistors were batch-processed by photoengrave etching on large wafers of silicon and then cut apart to produce the individual transistors, only to be soldered to other components on circuit boards inside the devices. Although expertly wired and soldered by the nimble fingers of legions of young women, the sheer number of wires in the ever-smaller devices was fast becoming intractable, particularly for the hundreds of thousands of wiring connections for the tens of thousands of transistors required for the ever more powerful and versatile mainframe computers.⁸

数字计算机的巨大潜力实际上被连接晶体管的复杂线路所扼杀；“数字暴政”抑制了伟大新机器的自由。

The great potential of the digital computer was being literally strangled by the tangle of wiring connecting the transistors; a “tyranny of numbers” suppressing the freedom of the great new machines.

来解放计算机的不是革命领袖，而是意大利烹饪艺术的厨师。为了避免将晶体管肉丸连接起来的意大利面条缠结^在一起，人们可以简单地做千层面。9

Coming to liberate the computers was not a revolutionary leader, but chefs of the Italian culinary arts. To avoid the tangled webs of wiring spaghetti connecting the transistors meatballs, one could simply make lasagna instead.⁹

有源硅半导体晶体管肉丸和连接线意大利面条可以集成到肉层组件和由二氧化硅奶酪层隔开的金属布线面条层中。

The active silicon semiconductor transistor meatballs and the connecting-wire spaghetti could be integrated into meat layer components and a layer of metal wiring pasta separated by layers of silicon dioxide cheese.

有源晶体管、无源电阻器和电容器均由沙漠基底上的单个半导体“台面”制成，所有不同的组件都集成在一个整体中^。10

The active transistors and passive resistors and capacitors were all fabricated from single semiconductor “mesas” on a desert substrate, a monolith of all the different components into a single body.¹⁰

因此在 1958 年，为了展示自己的才华，杰克·基尔比 (Jack Kilby) 打开了他的单片相移振荡器，将直流电转换为交流信号，当德州仪器的老板们看到直线电压在在线示波器显示屏上急剧变为正弦波时，他很容易就给老板留下了深刻的印象。

Thus in 1958, with a nod to showmanship, Jack Kilby turned on his monolithic phase-shift oscillator that converted a DC into an AC signal and easily impressed his Texas Instruments bosses as they watched the straight-line voltage dramatically change to a sine wave on the in-line oscilloscope display.

虽然资金很快就到了，但是，为了急于提交专利申请，基尔比使用了“飞线”图，将所有复杂的线路连接都暴露在外，而且他的原型也没有正确地声称任何集成的线路连接。

Funding was immediate, but in the rush to file a patent application, Kilby used a “flying wire” drawing with all the gangly wiring connections exposed, and his prototype did not properly claim any integrated wiring connections.

同年，这些飞线被蒸发并嵌入金属层，该金属层渗透到 SiO ₂绝缘层中预先蚀刻的微小孔中，形成平面半导体层的印刷电路导电通道。Fairchild Semiconductor 的 Robert Noyce 因此可以演示一种适用于计算机的双态触发器集成电路，它不仅省去了数千根电线的繁琐焊接工作，而且由于元件之间的距离只有微米，而电信号的传播速度只有光速的一半，触发器开关预示着超高速集成电路时代的到来^。11

In the same year, those flying wires were evaporated and embedded as a metal layer that seeped through tiny holes pre-etched in the SiO₂ insulating layer to form printed circuit conduction channels for the planar semiconductor layers. Robert Noyce at Fairchild Semiconductor thus could demonstrate a two-state flip-flop integrated circuit ideal for computers that not only obviated the tedious soldering of thousands of wires, but with the micron distances between components and electrical signals traveling at about half the speed of light, the flip-flop switch heralded the age of the superfast integrated circuit.¹¹

很快，随着 TI 的动态和静态随机存取存储器(DRAM 和 SRAM) 以及仙童公司和后来的英特尔的中央处理器(CPU) 的出现，计算机内存容量增加了几个数量级，它们分别成为即将出现的新型个人计算机的孤岛和主力。

Quickly, computer memory capacity increased by orders of magnitude with TI's dynamic and static random access memory (DRAM and SRAM) and Fairchild and later Intel's central processing units (CPUs) that respectively would become the silos and workhorses of the new personal computers that were looming on the horizon.

数字计算机终于摆脱了布线的束缚，数以百万计的晶体管和元件现在可以集成并作为完整的电子实体插入主板。开关和放大器的尺寸逐渐从相对笨重、发热的玻璃壁三极管缩小到凉爽的点接触晶体管，再到结型晶体管，最后到完全集成的晶体管电路。

The digital computer was at last free from its wiring bondage, millions of transistors and components now could be integrated and inserted on motherboards as complete electronic entities. The sizes of the switches and amplifiers progressively shrank from the relatively massive, hot glass-walled triode vacuum tubes to the cool point-contact transistor, to the junction transistor, and finally to the completely integrated transistor circuits.

数字的暴政被单片集成所克服，晶体管新技术催生出的大批熟练的年轻女焊工被自动化半导体平面工艺制造的新技术所解放，这便是机器取代人类的经典故事。

The tyranny of numbers was overcome by a monolithic integration, and the legions of skilled young women solderers spawned by the new technology of transistors were set free by the newer technology of automated semiconductor planar-process fabrication in an oft-repeated tale of machines replacing humans.

1963 年发明的低噪声、低温运行、零伏静态功耗（仅在0到1之间交替时才需要电压）、薄栅极互补金属氧化物半导体(CMOS) 很快就占据了主导地位，它“补充”了n型 (NMOS) 和p 型(PMOS) 晶体管，可以在晶圆上按照密集的设计规则形成，从而降低了尺寸和价格，不受摩尔定律的影响^。12

Invented in 1963, the soon to be dominant low-noise, cool-running, zero-volt static power (needs voltage only when alternating between 0 to 1), thin-gate Complementary Metal-Oxide Semiconductor (CMOS) that “complemented” n-type (NMOS) and p-type (PMOS) transistors could be formed under dense design rules on a wafer bringing down sizes and prices in abeyance to Moore's Law.¹²

CMOS 很快就成为个人电脑中几乎所有集成电路的主力半导体，并且薄膜版本用于液晶显示器，使笔记本电脑、平板电视和壁挂式电视成为可能。CMOS 传感器还取代了光学传感器和数码相机中更昂贵的电荷耦合器件 (CCD)，事实上，LCD 使手机成为可能，它不仅使持续的电话联系成为可能，而且使即时信息、音乐和叫车成为可能，同时为人工智能的训练集积累大数据。

The CMOS would soon become the workhorse semiconductor for almost all the integrated circuits employed in personal computers, and in the thin-film version used in liquid crystal displays that made possible the notebook computer, flat-panel monitors, wall-hanging television sets. CMOS sensors also replaced the more expensive Charge-Coupled Devices (CCDs) in optical sensors and digital cameras, and indeed the LCD made possible the mobile phone, which not only made possible continuous telephone contact, but also instant information, music, and ride-hailing, all the while amassing Big Data for the training sets of artificial intelligence.

20 世纪 60 年代末，在彻底击败雷明顿·兰德公司，并击退了当地竞争对手控制数据公司 (CDC)、数字设备公司 (DEC) 以及阿姆达尔，当时还有日本的 NEC 和富士通之后，IBM 的 System/360 集成电路计算机将其大型机霸权扩展到了世界的各个角落。

In the late 1960s, after soundly defeating Remington Rand and fending off local rivals Control Data Corporation (CDC), Digital Equipment Corporation (DEC), and Amdahl, then Japan's NEC and Fujitsu, IBM's System/360 integrated circuit computers extended its mainframe hegemony to all corners of the world.

然而，在北加州的硅谷，一场巨大的变化很快不仅导致计算机尺寸缩小，而且 IBM 本身也缩减了尺寸。

Off the silicon shores of Northern California, however, a sea change soon would not only downsize computers, but also IBM itself.

世界上第一台微处理器是 2250 个晶体管的 4 位英特尔 4004，于 1971 年为日本计算器制造商 Busicom 制造。1972 年的后续版本 8008 微处理器将 8 位字节排列成 256 个唯一的 1 和 0 阵列，可以处理十个数字、所有字母、标点符号和其他符号，在转换为 NMOS 之后，速度更快的 8080 微处理器与其竞争对手 Zilog 的 Z80 一起成为 Altair 等自制计算机套件的核心，供十几岁的男孩摆弄。

The world's first microprocessor, the 2250 transistors 4-bit Intel 4004 was made for the Japanese calculator maker Busicom in 1971. A later version in 1972, the 8008 microprocessor arranged 8-bit bytes into 256 unique arrays of ones and zeros that could handle the ten numerical digits, all the letters of the alphabet, punctuation marks, and other symbols, and after conversion to NMOS, the faster 8080 microprocessor, together with its competitor Zilog's Z80, was the heart of home-build computer kits such as Altair for teenage boys to tinker with.

在这些年纪较大的男孩中，史蒂夫·沃兹尼亚克 (Steve Wozniak) 于 1976 年制造出了第一台通用、紧凑、独立的家用计算机，而史蒂夫·乔布斯 (Steve Jobs) 大力推广其衍生产品 Apple II，以至于迫使不情愿的 IBM 带着其 PC 加入了个人计算机大军。PC 是一个开放系统，实际上是出于对反垄断调查的担忧而强制要求的，因此采用了英特尔的 CPU、TI 的内存和初创公司微软的操作系统。

Among those older boys, Steve Wozniak built the first general-purpose, compact, stand-alone home computer in 1976, and Steve Jobs promoted the derivative Apple II so aggressively as to force a reluctant IBM to join the personal computer parade with its PC, an open system effectively mandated by fear of Antitrust investigation, and so run by CPUs from Intel, memory from TI, and an operating system from start-up Microsoft.

开放系统允许康柏公司进行克隆，也允许新制造商降低价格，例如台湾的宏碁，它们以自己的品牌在世界各地销售个人电脑，但大多是作为几乎所有其他品牌的 OEM，包括 IBM、戴尔、惠普、东芝和索尼^。13

The open system allowed cloning by Compaq and price reduction by new manufacturers such as, Acer in Taiwan, who sold PCs all over the world under their own brands but mostly as OEMs for almost all the other brands, including IBM, Dell, HP, Toshiba, and Sony.¹³

虽然超薄笔记本电脑的功能已经远远超越了早期体积庞大的大型机，但物理和化学量子力学、天体物理学、流体动力学、天气预报、物理和工程模拟以及人工智能大数据的多参数、相互依赖、非线性微分方程的大规模并行计算需要更快的计算机速度和功率。

While the capabilities of even super-thin notebook computers have already far surpassed the bulky early acronymic mainframes, much greater computer speed and power are required for the massively-parallel calculations of the multi-parameter, interdependent, non-linear differential equations of physical and chemical quantum mechanics, astrophysics, fluid dynamics, weather prediction, physical and engineering simulations, and indeed the Big Data of artificial intelligence.

最近，超级计算机已用于分子和遗传建模、密码分析、宇宙起源的宇宙学计算，现在还用于病毒和气候变化模型的生物系统模拟；它们可以而且很可能很快就会用于总体人工智能。

More recently, supercomputers have been used in, molecular and genetic modeling, cryptanalysis, cosmological calculations of the beginning of the Universe, and now crucially in biological system simulations of viruses and climate change models; they can and likely soon will be used in overarching artificial intelligence.

例如，天体物理学家需要 3000 年才能解出恒星从诞生到死亡的演化方程，而超级计算机只需几秒钟就能完成。更近一点，核武器爆炸模拟可以让拥有核武器的交战国只需交换模拟打印输出和计算机图形，就能确定谁的炸弹更具破坏性，将战争从战场带到实验室，只要世界领导人懂点科学就行了^。14

For example, solving the equations of stellar evolution for a star from birth to death would take an astrophysicist 3,000 years, while a supercomputer can do it in seconds. Closer to home, simulations of nuclear weapons explosions could allow nuclear-armed belligerents to just exchange simulation print-outs and computer graphics to determine whose bomb was more destructive, bringing warfare from the battlefield to the laboratory, if only world leaders knew something about science.¹⁴

20 世纪 70 年代，控制数据公司和 Cray Research 开始争夺世界最快计算机的头衔。最初，CDC 和 Cray 几乎是孤军奋战，先是日本 NEC 和富士通，然后是中国的神威和天河，后两家最​​近又与美国的 IBM Summit 和 Sierra 轮流争夺全球超级计算机霸主地位。

In the 1970s, Control Data Corporation and Cray Research began the race for the title of world's fastest computers. Initially virtually alone in the field, CDC and Cray met competition first from Japan's NEC and Fujitsu, then later from China's Sunway and Tianhe, the latter two recently taking turns with America's IBM Summit and Sierra in the race for global supercomputer supremacy.

2018 年，巅峰超级计算机以每秒 122.3 千万亿次浮点运算的 HPL 基准从神威超级计算机手中夺回了王冠，但中国的超级计算机在 2018 年超级计算机排名中占据了前 500 名中的 227 个，其中还包括来自日本、法国和德国的超级计算机。在执行有用的科学和工程模拟的同时，超级计算机也成为国家技术实力的象征。

Summit regained the crown from Sunway in 2018 with an HPL benchmark 122.3petaflops, but China's supercomputers claimed 227 of the top 500 in the 2018 supercomputer rankings, that also included supercomputers from Japan, France, and Germany. While performing useful scientific and engineering simulations, the supercomputers have also become symbols of national technological prowess.

运行超级计算机的大规模并行处理器核心主要来自 IBM、英特尔、神威、富士通、ARM 和 Nvidia，设计架构来自各个超级计算机实体，其中包括许多大学、研究机构和半公共机构^。15

The massively-parallel processor cores running the supercomputers were primarily from IBM, Intel, Sunway, Fujitsu, ARM, and Nvidia, and the design architectures were from the individual supercomputer entities which included many universities, research institutions, and semi-public concerns.¹⁵

这些惊人的速度和能力，加上大数据和深度人工神经网络，不禁让人联想到令人不安的画面：一台超级计算机控制着一支庞大的通用机器人大军，在人类文明中肆虐，或者至少在不久的将来，实现所有制造和服务的自动化，并监控人们在家中和工作场所的状态，同时控制美国、中国、欧洲乃至全世界道路上和轨道上的几乎所有车辆。

These fantastical speeds and capabilities, combined with Big Data and deep artificial neural networks cannot help but evoke disturbing images of a supercomputer controlling a vast army of general-purpose robots running rampant over human civilization, or at least in the very near future, automating all manufacturing, services, and monitoring humans at home and at work, together with controlling almost all the vehicles on the roads and tracks of first America, China, Europe and then the whole world.

电视雅卡尔织布机的打孔卡指示机器如何织布，洛夫莱斯伯爵夫人的打孔卡指示巴贝奇的分析机如何计算，布尔的二进制代数指示计算机如何计算。机器可以理解这些指令集，然后可以将其视为用机器语言编写的。

The punch-hole cards of Jacquard's loom instructed the a machine to weave cloth, the Countess of Lovelace's punch-hole cards instructed Babbage's Analytical Engine how to calculate, and Boole's binary algebra instructed a computer how to compute. The machines could comprehend these instruction sets which then could be seen as written in a machine language.

在二进制计算机中，由零和一组成的编码字符串构成指令，例如，在 8 位指令中，前四位可能告诉计算机要做什么，而后四位告诉它可以在哪里找到要使用的数据。

In a binary computer, encoded strings of zeros and ones constituted the instruction where, for example, in an 8-bit instruction, the first four bits may tell the computer what to do and the last four bits tell it where the data to use can be found.

计算机基本操作超过 200 种，因此用机器语言编码和跟踪所有指令集是一场噩梦，更糟糕的是，不同的机器有不同的设计和结构，即使它们相似，也没有程序步骤顺序和寄存器地址的规则，因此，即使是用机器语言为某台机器编写的程序，也无法转移到另一台机器上。

There are more than 200 fundamental computer operations so encoding and keeping track of all the instruction sets in machine language was a nightmare, made worse by the fact that different machines would have different designs and structures, and even if they were similar, there were no rules for program step sequences and register addresses, so a program written for one machine, even in machine language, was not transferable to another machine.

计算逻辑问题已经被图灵和冯·诺依曼解决了，但用机器语言编程的实际实现却非常困难，而且容易出错，编写的程序无法在不同的机器上使用，甚至程序员自己事后也几乎无法理解。

The computational logic problem had been solved by Turing and von Neumann, but the practical implementation of programming in machine language was difficult and error-prone, the programs could not be used on different machines, and were almost impossible to understand even by the programmers themselves after the fact.

这为软件通用化提供了动力，UNIVAC 项目的助理 Grace Hopper 被 John Mauchly 指派使他们的新机器二进制自动计算机（BINAC）能够接受用户编写的代数方程。

This provided the impetus for software generalization, and Grace Hopper, an assistant on the UNIVAC project, was assigned by John Mauchly to make their new machine, the Binary Automatic Computer (BINAC), capable of accepting algebraic equations as written by the user.

霍珀立刻意识到“人们可以使用机器代码以外的某种更高级的代码”来对计算机进行编程，这种代码更容易被人类理解，计算机可以将其翻译成机器语言，以供计算机翻译和阅读。

Hopper realized at once that “one could use some kind of higher code other than the machine code” to program a computer, a code that was more easily understood by humans that could be translated by the computer into machine language for the computer to translate and read.

由于在操作过程中许多过程和数学计算都会重复进行，Hopper 和同事们设计了简短的命令助记符，例如 LOAD、STORE 和 PRINT，并将它们与相关的机器语言指令集及其组合相关联，以便可以使用简单的命令来调用所需过程的执行。

Since many processes and mathematical computations are repeated during an operation, Hopper and co-workers devised short command mnemonics such as LOAD, STORE, and PRINT, associating them with the relevant machine language instruction sets and combinations thereof, so that simple commands could be used to call up the performance of a desired process.

这些子程序还包括数学计算，例如求平方根 (SQRT)，一旦用机器语言汇编，就可以存储在子程序库中，当与其他操作一起编译时，程序员可以使用简短的助记符命令调用这些命令来执行计算。使用这种汇编语言汇编的此类命令序列比机器语言更容易编写，也更容易让其他人理解^。1

These subroutines also included mathematical computations, for example taking a square root (SQRT) that, once assembled in machine language, could be stored in a subroutine library, and when compiled with other operations, could be called up by the programmer using the short mnemonic commands to perform the calculation. A sequence of such commands assembled using this assembly language was easier than machine language for someone to write and others to understand.¹

这些子程序一旦在计算机中编译完成，任何人都可以使用它们来编写汇编语言程序，而机器只需访问所调用的机器语言指令集，即可将汇编语言翻译成机器语言。1952 年，霍珀将语言翻译称为编译，将翻译器称为编译器，这些术语至今仍在使用。

These subroutines once compiled in the computer could then be used by anybody to write programs in assembly language, with the machine doing the work of translating from assembly language to machine language by simply accessing the called-upon machine language instruction sets. Hopper in 1952 called the language translation compiling, and the translator was called a compiler, terms that are still in use today.

在她为海军研究哈佛 Mark I 的后继者期间，Mark II 神秘地崩溃了。经过调查，霍珀发现，一只飞蛾误入了迷宫般的电路，并因阻塞了导致故障的电继电器开关而死亡。因此，“调试计算机”一词成为了任何计算机故障的代名词。

During her work for the Navy on the successor to the Harvard Mark I, the Mark II mysteriously crashed, and upon investigation, Hopper found that a moth had wandered into the maze of circuitry and died in shock blocking an electric relay switch that caused the malfunction. And so the term “debugging the computer” became the term for any computer malfunction.

尽管汇编语言比机器语言更容易掌握和使用，但它仍然需要指定地址寄存器，并了解所有可能因机器而异的简短指令助记符；它还需要对每个机器的设计和工作原理。因此，下一步是制定一种更易于编写和理解的高级语言，然后让计算机使用编译器将该语言翻译成汇编语言，然后再翻译成机器语言。

Although much easier to master and use than machine language, assembly language still required designating address registers and knowing all the short instruction mnemonics which may vary from machine to machine; it also still required an intimate knowledge of each machine's design and workings. The next step thus was to formulate a higher-level language that was easier to write and understand, and again have the computer translate that language into assembly language and then into machine language, using compilers.

1957 年，IBM 软件开发先驱 John Backus 创建了 FORTRAN（公式翻译），该语言可在新型 IBM 704 上编译使用，从高级语言到汇编语言，最后到机器语言。FORTRAN 使用相对自然的语言语句，将多个汇编语言和机器语言指令卷积为单个语句，这些语句可以命令计算机执行主要的科学和工程计算。

Software development pioneer John Backus at IBM in 1957 created FORTRAN (Formula Translation) that could be compiled for use on the new IBM 704, going from high-level to assembly, and finally to machine language. FORTRAN employed relatively natural language statements that convolved several assembly and machine language instructions into single statements that could command a computer to perform mainly scientific and engineering calculations.

当计算机启动时，内置程序会指示 CPU 找到操作系统，然后操作系统将控制系统硬件；一些功能程序会永久存储在 ROM 中，CPU 会使用编译器将高级语言计算机程序翻译成汇编语言，然后执行机器语言指令；RAM 通常用于在处理过程中保存信息和程序。

When a computer is turned on, built-in programs instruct the CPU to find the operating system which then takes control of the system hardware, a few functional programs are permanently stored in the ROM and the CPU executes the instructions in machine language after being translated from a high-level language computer program through an assembly language using a compiler; a RAM typically holds information and programs during processing.

通用商业导向语言(COBOL)主要用于商业用途，它能够更高效地对大量数据进行归档、排序、合并、添加、减去和计算百分比，并方便地生成报告，所有这些都使用句法英语。COBOL 仍然被企业使用，并且通常是存储在许多公司的大型机档案中以供参考的遗留语言。

Primarily for business and commercial use, the Common Business Oriented Language (COBOL) could more efficiently file, sort, merge, add, subtract, and calculate percentages over large sets of data, and conveniently generate reports, all using syntactical English. COBOL is still used by businesses and often is a legacy language stored in many companies’ mainframe archives for reference.

作为 COBOL 的句法性质和普遍性的一个例子，当 Grace Hopper 被困在日本的一个计算机中心时，她很难向不会说英语的日本程序员表达她想回到酒店的愿望，于是她求助于 COBOL，指着自己说“MOVE”，然后指着中心外面说“GOTO Osaka Hotel” ^。2

As an example of the syntactical nature and universality of COBOL, when Grace Hopper was stranded at a computer center in Japan, and having difficulty in communicating her wish to go back to her hotel to the non-English speaking Japanese programmers, she resorted to COBOL, pointing to herself and saying “MOVE”, and then pointing outside the center, said “GOTO Osaka Hotel”.²

算法语言(ALGOL)主要在欧洲设计，旨在更符合计算机科学的基本语法原则，表面上是为了比 FORTRAN 更优雅地进行数学计算，但实际上它是欧洲对抗美国 FORTRAN 霸权的假定手段。毫不奇怪，ALGOL一度成为欧洲开发软件的通用语言，但由于缺乏由于内置了诸如标准化输入/输出机制之类的实用程序，FORTRAN 在大多数新软件编写的美国仍然占据主导地位。

Primarily in Europe, the Algorithmic Language (ALGOL) was designed to be more in tune with fundamental computer science syntactical principles ostensibly to do mathematical computation more elegantly than FORTRAN, but in truth was Europe's putative counter to America's FORTRAN hegemony. Not surprisingly, ALGOL became the lingua franca for European-developed software for a time, but for lack of built-in utilities such as a standardized input/output regime, FORTRAN still held sway in America where most new software was written.

所有这些语言都是基于命令式编程方法，即程序在任何时候都有一个隐式状态，定义所有变量的值和当前控制点，并且当程序通过冯·诺依曼架构执行时，程序员可以通过检查程序的转储文件了解计算机经过的每个步骤和状态。

All these languages were based on the imperative programming approach that at any time the program has an implicit state defining the values of all the variables and current point of control, and as the program executes by means of the von Neumann architecture, the programmer can know each and every step and state through which the computer passes by examining the program's dump files.

命令式编程的主要数学逻辑和操作功能在面向对象编程方法中扩展为对象，该方法通过将数据和指令分组为模块化对象的直接和显式表示来模拟系统，这些模块化对象具有一组指令和相关的离散数据部分，每个数据部分代表给定系统运行的一个方面。

The primarily mathematical logic and operational functions of imperative programming were expanded to objects in an object-oriented programming approach that simulated systems by grouping data and instructions into direct and explicit representations of modular objects having a set of instructions and relevant discrete portions of data each representing one facet of a given system run.

例如，银行程序会定义诸如储蓄、支票和定期存单账户之类的对象，以及诸如余额、利息、银行费用等概念；而电子工程程序会定义诸如电阻器、电容器和晶体管之类的对象，以及诸如电阻、电容和栅极电压之类的概念，然后按照操作指令对对象进行分类和比较。面向对象语言后来被用C++、Java、Python 和 JavaScript编写的人工智能程序所采用。

For examples, a banking program would define objects such as savings, checking, and certificate of deposit accounts, and concepts such as balance, interest, bank charges, and so on, while an electrical engineering program would define objects such as resistors, capacitors, and transistors, and concepts such as resistance, capacitance, and gate voltage, and then following operation instructions, classifying and comparing the objects. Object-oriented languages would later be employed by artificial intelligence programs written in C++, Java, Python, and JavaScript.

高级语言计算机编程从以 FORTRAN 为主的批处理模式计算机打卡机，发展到远程哑终端分时，再到纸带指令的 PDP 系列等小型计算机，再到英特尔微处理器运行的 BASIC Altair 微处理器，再到可以通过互联网访问任何语言的个人计算机，最后发展到在线主机编码平台（如GitHub），其中更直接控制的C++语言和更高级的 Python 和 Java 在新程序的制作中占主导地位，源代码已发布并免费分发。这种开源软件（OSS）是人工智能发展的重要资源。

High-level language computer programming progressed from the mainly FORTRAN batch-mode computer punch-card to remote dumb terminal time-sharing, and then to minicomputers like the paper-tape instructed PDP series, to the Intel microprocessor-run BASIC Altair microprocessor, to personal computers that can access any language over the Internet, and finally to online host-computer coding platforms such as GitHub where the more direct control C++ language and the higher-level Python and Java are dominant in the production of new programs with source code published and freely distributed. This open source software (OSS) was a critical resource for the development of artificial intelligence.

电视第一个远距离电子通信是塞缪尔·莫尔斯的三态（关、点、划）三进制系统，代表字母表中的字母，这些字母的组合可以形成单词和消息。信号通过专用传输线发送，但尽管成功了，但它只能按顺序一次发送一条消息，因此在作为远程通信系统的使用方面非常有限。为了携带更多的消息，埃米尔·鲍多想到改变不同消息状态之间的时间，允许消息通过其频率进行区分并在同一线路上同时发送。

The first electronic communication over distance was the three-state (off, dot, dash) trinary system of Samuel Morse representing letters of the alphabet which combinations thereof could form words and a message. The signals were sent over dedicated transmission lines, but although successful, it could only send messages sequentially one at a time and was so limited in its use as a long-range communications system. To carry more messages, Emile Baudot thought of changing the time between states for different messages, allowing the messages to be differentiated by their frequency and sent simultaneously over the same line.

这种多路复用的概念被用于专用线路上的机器通信，在两状态（开、关）二进制编码电报中，使用电传打字机和五位波特码来立即传输消息，或将消息记录在纸带上以便延迟传输或存储。

This concept of multiplexing, was employed for machine communications over dedicated lines, in the two-state (on, off) binary-coded telegraph using a teletypewriter and a five-bit Baudot code to instantly transmit messages, or record messages on paper tape for delayed transmission or storage.

1876 年，亚历山大·格雷厄姆·贝尔 (Alexander Graham Bell) 制造了一个与松散碳粒袋接触的振动膜，并在其中通入直流电流，因此当声音振动振动膜时，它将影响碳粒，从而改变碳粒在袋中的密度，从而调节电流，从而产生代表声音的电流。因此，“语音”电流可以通过一根缠绕在与振动膜接触的电磁铁上的电线传输到目标接收器，振膜将根据语音电流振动，从而在目的地重新形成语音。

Alexander Graham Bell in 1876, constructed a diaphragm in contact with a bag of loose carbon particles and ran a dc current through it, so when a sound vibrates the diaphragm, it will impact the carbon particles changing their density in the bag thereby modulating the current, thus producing an electric current that represents the sound. Thus a “voice” current can be transmitted to a destination receiver in a wire which is wrapped around an electromagnet in contact with a diaphragm, the diaphragm will then vibrate in accord with the voice current thus reforming the speech at the destination.

多路复用允许通过一条线路同时传输电话呼叫。如今，通过不同频率进行多路复用称为频分多址(FDMA)，通过编码消息进行划分称为码分多址(CDMA)（GPS 全球定位系统使用这种技术），使用分配的时隙进行划分称为时分多址(TDMA)，使用传输线路两端的同步开关划分消息称为同步分多址(SDMA)。除此之外，还有许多不同多路复用方案的变体和组合，例如欧洲使用的串联 TDMA/FDMA全球移动通信系统(GSM) 和中国使用的双工同步时分/码分系统，称为 TD-SCDMA。

Multiplexing allowed simultaneous transmission of telephone calls over a single line. Today the multiplexing by different frequencies is called frequency-division multiple access (FDMA), division by coding messages is called code-division multiple access (CDMA) (which is used by the GPS Global Positioning System, using allocated time-slots is time-division multiple access (TDMA), and using synchronized switches at each end of the transmission line to divide messages is called synchronous-division multiple access (SDMA). In addition to all that, there are many variations and combinations of the different multiplexing schemes as used for example in Europe the tandem TDMA/FDMA Global System for Mobile (GSM) and in China a duplex synchronous time/code-division system called TD-SCDMA.

对于互联网通信，早期有线以太网使用空分多址(SDMA) ，而 IEEE802 系列标准协议用于局域网 (LAN)、WiFi 和互联网访问的无线路由。电磁波具有极化能力，例如用于无绳电话、数字无线电、ADSL 和 LTE 的极化多址(PDMA)，从而提高了速度。对于通过光纤电缆进行的互联网传输，使用波分多址(WDMA) ^。1

For Internet communication, space-division multiple access (SDMA) is used on the early wired Ethernet and the IEEE802 family of standard protocols was used for wireless routing for local area networks (LANs), WiFi, and accessing the Internet. Improved speed was provided by the capability of electromagnetic waves to be polarized as in polarized-division multiple access (PDMA) which was used for cordless telephones, digital radio, ADSL and LTE. For Internet transmission over fibre optic cables, wave-division multiple access (WDMA) is used.¹

对于 4G 和 5G 移动设备通信，包括移动电话、自动驾驶汽车、机器人和许多其他通信系统，使用正交频分多址(OFDMA)，然而多址会导致载波间干扰(ICI，串扰)，因为子载波的频率偏差会影响极化正交性，因此必须单独对每个子载波进行整形，以防止子载波频率重叠。毋庸置疑，各种复用对于处理电子通信的爆炸式增长至关重要^。2

For 4G and 5G mobile device communications, including mobile phones, autonomous cars, robots, and many other communication systems, orthogonal frequency-division multiple access (OFDMA) is used, however multiple access causes inter-carrier interference (ICI, cross-talk) because frequency deviations of the sub-carriers will affect the polarization orthogonality, so each sub-carrier must be individually shaped to prevent sub-carrier frequency overlapping. Needless to say, all kinds of multiplexing were essential for handling the explosive growth of electronic communications.²

语音电子通信通过将信息分成可以在最短时间内同时发送的数据包来有效地传输。繁忙的线路，然后在目的地重新组装以重新形成消息，这一过程称为分组交换。

Voice electronic communications are efficiently transmitted by dividing them into packets that can be simultaneously sent over the least busy lines and then reassembled at the destination to re-form the message in a process called packet-switching.

早期的个人计算机通信是通过电话线进行的，通过调制发送器上的载波到接收器调制解调器，传输速率称为波特率（以纪念 Baudot）。几年后，任何人都会记得处理不稳定的调制解调器通信时的惊慌失措。

Early personal computer communication was carried by telephone lines through modulation of a carrier wave at the transmitter to the receiver modem at a rate of transmission called the baud rate (in honor of Baudot). Anyone of a few years will remember the consternation of dealing with unstable modem communications.

直接有线的计算机间通信比电话线传输更快、更可靠，但一开始直接有线的计算机只能通过其主机网络服务器进行通信，并且由于每个主机网络服务器的通信操作系统可能不兼容，因此并非所有计算机都可以相互通信。

Directly-wired inter-computer communications were much faster and more reliable than the telephone line transmissions, but in the beginning directly-wired computers could only communicate through their host network server, and since each host network server communication operating system may not be compatible, not all computers could communicate with each other.

个人计算机之间的通信显然需要监督、监管和制定标准。兼容通信的规则由互联网工程任务组(IETF) 制定，这是一个松散的非营利组织，任何人都可以通过该组织贡献专业知识来形成协议，例如互联网协议(IP)、超文本传输​​协议(HTTP) 和简单邮件传输协议(SMTP)，这些协议规定了计算机间通信的形式、传输速率和错误检查方法。此后，每个主机服务器通信操作系统都必须遵循协议才能相互通信，从而事实上要求计算机间通信的传输标准化^。3

Oversight, regulation, and standards-setting were clearly necessary for personal computer inter-communications. Rules for compatible communicating were set by the Internet Engineering Task Force (IETF), a loose non-profit organization through which anyone can contribute expertise to form protocols such as the Internet Protocol (IP), Hypertext Transfer Protocol (HTTP), and Simple Mail Transfer Protocol (SMTP), which dictated the form, transmission rate, and error-checking methods for inter-computer communication. Each host server communication operating systems thereafter was obligated to follow the protocols in order to communicate with each other, thereby de facto mandating transmission standardization for inter-computer communication.³

早期的形式协议包括美国信息交换标准代码(ASCII)，它是 128 个字符串的编码系统，每个字符串由七个 1 和 0 组成，每个序列代表一个阿拉伯数字、一个英文字母、标点符号、符号和键盘 ENTER 等操作，于 1963 年成为所有计算机的通用标准。

Among the earlier protocols for form was the American Standard Code for Information Interchange (ASCII), the coding system of 128 strings of seven ones and zeros, each sequence representing an Arabic numeral, a letter of the English alphabet, punctuation marks, symbols, and actions such as keyboard ENTER, became the universal standard for all computers in 1963.

在计算机时代的初期，计算机都是集中式大型机批处理和现场分时终端需要用户长途跋涉到计算机中心才能使用计算机。“计算机时间”是一种收费的提议，虽然它可能提高了程序效率，但也可能因为“计算机费用”而阻止一些人根本不使用主计算机。

In the beginning of the computer age, the computers were all centralized mainframe batch-processing and on-site time-share dumb terminals that required the user to trek to the computer center to use the computer. “Computer time” was a fare-based proposition charging for use, and although it may have improved program efficiency, it may also have dissuaded some to not use the main computer at all because of the “computer charges”.

早在1961年，麻省理工学院人工智能实验室的联合创始人约翰·麦卡锡就建议在IBM 709上进行远程分时，该建议随后促成了美国国防部高级研究计划局于1969年建立的阿帕网，连接了犹他州和加利福尼亚州的国防工作研究实验室，这是第一个功能齐全的分组交换网络，它的后代对于人工智能开发人员之间的交流至关重要。

Earlier, in 1961, John McCarthy, a co-founder of the MIT Artificial Intelligence Laboratory, suggested remote time-sharing on the IBM 709, and the proposal subsequently led to the Department of Defense Advanced Research Project Agency's ARPANET in 1969 linking defense-work research laboratories in Utah and California, this was the first fully-functional packet-switched network whose progeny would be critical for the communication among the developers of artificial intelligence.

随着分布式计算能力的出现，分布式计算机的概念也随之而来。数字设备公司 (DEC) 的一系列新推出的小型计算机（他们称之为可编程数据处理器(PDP-n)）以及惠普、霍尼韦尔和通用电气等其他公司满足了这一需求。这些小型计算机没有大型机的处理能力，但它们更小、更便宜，并且可以针对各个实体的项目的特定任务进行编程，也可以链接到大型机。

With the advent of distributed computing power came the idea of distributed computers themselves. The demand was met primarily by the Digital Equipment Corporation's (DEC) series of newly-coined minicomputers in a series they called Programmed Data Processors (PDP-n), and by other companies such as Hewlett-Packard, Honeywell, and General Electric. The minicomputers did not have a mainframe's processing power, but they were smaller and cheaper, and could be programmed for specific tasks for the projects of the individual entities, as well as linking to a mainframe.

但当时每家公司的小型计算机都有自己独特的设计和操作系统，因此必须用汇编语言为每台小型计算机从头编写程序，如果公司或部门升级或更换到不同供应商的小型计算机，所有旧程序和例程都将毫无用处，必须重新编写才能在新的小型计算机上使用。

At the time, however, each company's minicomputer came with its own specific design and operating systems, so programs for it had to be written from scratch in assembly language for each minicomputer, and if a company or department upgraded or changed to a different vendor's minicomputer, all the old programs and routines were useless and had to be re-written for use on the new minicomputer.

在贝尔实验室，研究员肯·汤普森的太阳系模拟程序被加载到一台图形效果良好的 PDP-7 上，但令他苦恼的是，这台小型计算机缺少复印和打印等基本实用程序，因此他和同事丹尼斯·里奇用汇编语言编写了实用程序，并添加了文件管理和文本编辑功能。然后，他们将这些例程加载到贝尔实验室新购买的一台 PDP-11 上，这台 PDP-11 比 PDP-7 速度更快，内存更大。

At Bell Labs, researcher Ken Thompson's Solar System Simulation program was loaded on a PDP-7 with good graphics, but that minicomputer to his chagrin lacked basic utility routines such as copy and print, so he and colleague Dennis Ritchie wrote the utilities in assembly language and added file management and text-editing. They then loaded these routines into one of Bell Labs’ newly-purchased PDP-11s that was faster with more memory than the PDP-7.

尽管汤普森的太空旅行图形给人留下了深刻的印象，但贝尔实验室的其他研究人员对实用程序更感兴趣，因此，为了响应许多请求，汤普森和里奇为 PDP-11编写了一个操作系统手册，称该系统为 UNIX，该系统于 1972 年升级为分时管理，并进一步扩展可容纳 100 个模块，用于记录仪器读数、排序、链接和分析数据，这些数据可以按顺序运行用户的特定研究程序。所有程序和实用程序都可以存储在单个 PDP-11 中，因此可以作为独立计算机满足研究人员的特定需求^。4

Although impressed by Thompson's Space Travel graphics, other researchers at Bell Labs were more interested in the utility routines, and so in response to many requests, Thompson and Ritchie wrote up an operating system manual for the PDP-11s, calling the system UNIX which was upgraded for time-share management in 1972, and further expanded to hold 100 modules for recording instrument readings, sorting, linking, and analyzing data that could be sequenced to run a user's specific research program. All the programs and utilities could be stored in a single PDP-11 and thus were available for a researcher's specific needs as a stand-alone computer.⁴

然而，贝尔实验室的大多数科学家和工程师都不知道如何用汇编语言编写计算机程序，更不用说机器语言了，因此汤普森和里奇编写了一种用于编写 UNIX 操作系统的高级语言，他们称之为“ C ”（作为当​​时使用的有限的Basic 组合编程语言“ B ”的后继者）。 C诞生于 1973 年，是C++语言的前身，现在广泛用于编写人工智能算法。⁵

Most of the scientists and engineers at Bell Labs, however, did not know how to write computer programs in assembly language, let alone machine language, so Thompson and Ritchie wrote a higher-level language for programming the UNIX operating system that they called “C” (as the successor to the limited Basic Combined Programming Language called “B” then in use). Born in 1973, C is the progenitor of the C++ language now widely used for coding artificial intelligence algorithms.⁵

1974 年，DEC以象征性的费用向使用 PDP 计算机的行业和大学授予了 UNIX 许可证，C 语言在价值 50,000 美元的 PDP-11 上发布，该机器装载了 UNIX，很快成为科学和工程领域事实上的标准分布式小型计算机。PDP-11 小型计算机不仅可以用作独立的多用途计算机，还可以使用中央内核管理数据和程序文件、控制实验室设备、文本编辑和数据格式化报告，并通过shell在多个本地和远程网络上进行分时和程序共享。

With a nominal-fee license for UNIX to industry and universities using PDP computers, the publication of C in 1974 on DEC's $50,000 PDP-11 loaded with UNIX soon became the de facto standard distributed minicomputer for science and engineering use. The PDP-11 minicomputer could not only serve as a stand-alone, multipurpose computer, it could manage data and program files, control laboratory equipment, text-edit and data-format reports using a central kernel, and through a shell, time-share and program-share over multiple local and remote networks.

伯克利于 1977 年建立了基于 UNIX 的自由开放的“主机编码平台”，称为“伯克利软件发行版”（BSD），它是今天GitHub和Red Hat等对人工智能发展至关重要的平台的先驱。

Berkeley in 1977 established a free and open “host-computer coding platform” based on UNIX called the “Berkeley Software Distribution” (BSD), the harbinger of today's platforms such as GitHub and Red Hat that are now critical for the development of artificial intelligence.

1978年，DEC 推出速度更快、功能更强大、内存为 4.3GB 的 VAX 11/780，成为工业、大学和研究机构的主流分布式计算机。

In 1978, DEC's faster and more powerful VAX 11/780 with 4.3 gigabytes of memory took over as the mainstream distributed computer for industry, universities and research institutions.

由于任何装有 UNIX 操作系统和C编译器的计算机都可以使用 UNIX 系统，因此到 1983 年，超过 80% 的大学计算机科学系都采用了免费的 UNIX 计算机间通信系统。

Since any computer with a UNIX OS and a C compiler could employ the UNIX system, so that by 1983 more than 80% of university computer science departments had adopted the free UNIX inter-computer communications system.

然而同年，美国司法部与 AT&T 的反垄断同意协议被解除，UNIX 突然成为商业产品需求量很大，而且由于源代码只能按原样授权，在商业计算机世界里走了很多路之后，几乎每一站都产生了许多不同版本的 UNIX，每个版本都有自己的特点，以前的标准通信格式被分割开来，减少了 UNIX 的覆盖范围。UNIX 的高价商业化导致了 Richard Stallman 的免费 G​​NU（“GNU 不是 UNIX”）的出现，下一章将对此进行描述。

However in the same year, the Department of Justice's antitrust consent agreement with AT&T was lifted and UNIX suddenly became a commercial product in high demand, and because the source code was only licensed as is, after much travelling through the commercial computer world, almost every stop produced many different versions of UNIX, each with its own idiosyncrasies, the erstwhile standard communications formats were Balkanized decreasing UNIX's reach. The the high-price commercialization of UNIX led to Richard Stallman's free GNU (“GNU is not UNIX”) to be described in the next chapter.

早在 1971 年，雷·汤姆林森 (Ray Tomlinson)就使用 @ 符号作为地址发送了第一封电子邮件，1973 年，用于机构和公司内部计算机连接的局域网(LAN) 开始使用大容量以太网同轴电缆共享数据和信息。

Way back in 1971, Ray Tomlinson sent the first email using the @ symbol for the address, and in 1973, the local area network (LAN) for computer connections within institutions and companies began using high-capacity Ethernet coaxial cables for sharing data and information.

1980 年，在斯坦福大学，计算机科学研究生 Leonard Bosack 想与女友 Sandy Lerner 进行计算机通信，后者也是计算机科学系的毕业生，当时负责管理斯坦福商学院计算机实验室。他们曾跋涉穿过校园地下维护隧道，拉起电缆连接他们的计算机，因此他们想出了使用路由器和服务器为斯坦福不同部门的计算机建立 LAN 连接的想法，并以此为基础于 1984 年成立了思科公司，为计算机联网提供硬件和软件^。6

At Stanford in 1980, Computer Science grad student Leonard Bosack wanted to computer-communicate with his girlfriend Sandy Lerner, also a Computer Science Department graduate, who was managing the Stanford Business School Computer Lab. They legendarily trudged through the underground cross-campus maintenance tunnels stringing cable to connect their computers, and so came up with the idea of routers and servers to make LAN connections for the different departmental computers at Stanford, the basis for starting a company in 1984 called Cisco to provide hardware and software for networking computers.⁶

为了进一步扩展广域网(WAN)，客户端计算机可以按照 1983 年的传输控制协议/互联网协议(TCP/IP) 访问分组交换服务器，该协议如今规定了如何将消息分解成数据包、进行分类、传输到 IP 地址（当前为IPv6）以及如何使用域名系统(DNS) 进行传输并在目的地重新组装。

To further expand wide area networks (WANs), client computers could access the packet-switching servers in accord with the 1983 Transmission Control Protocol/Internet Protocol (TCP/IP) that today governs how messages are broken up into packets, sorted, transmitted to IP addresses (currently IPv6) and transmitted using the Domain Name System (DNS), to be reassembled at the destination.

在接下来的几年里，欧洲核子研究中心的蒂姆·伯纳斯·李 (Tim Berners Lee)于1989 年推出了万维网，它通过统一资源定位符(URL)来识别网站，并使用超文本标记语言(HTML)进行链接，以便所有新兴的网络浏览器都可以访问互联网上的所有网站。

In the next few years in quick succession, Tim Berners Lee at CERN launched the World Wide Web in 1989 that identified websites by Uniform Resource Locaters (URLs) that were linked using Hypertext Markup Language (HTML) so that all the nascent web browsers could access websites all over the Internet.

伊利诺伊大学的 Marc Andreessen 于 1993 年开发了Mosaic，这是第一个供公众使用的通用网络浏览器，并共同创立了Netscape于 1995 年发明；华盛顿大学的 Brian Pinkerton 于 1994 年发明了用于通用互联网搜索的WebCrawler ( Spiderbot )，同年斯坦福大学的杨致远与 David Filo 推出了第一个树形结构的分级 Web 目录Yahoo。

Marc Andreessen at the University of Illinois developed Mosaic, the first general purpose web browser for public use in 1993 and co-founded Netscape in 1995; Brian Pinkerton at the University of Washington in 1994 invented the WebCrawler (Spiderbot) for universal Internet searching, and in the same year, Jerry Yang and David Filo at Stanford unveiled the first tree-structure hierarchical Web directory Yahoo.

每个人都知道研究生谢尔盖·布林和拉里·佩奇在斯坦福大学进一步开发网络爬虫的故事，以及 1998 年搜索引擎的故事，该搜索引擎将公司名称“Google”变成了在线搜索的动词。数据采集的革命和逐渐积累的数据量，例如 Google ImageNet的 1400 多万张带标签的图像作为计算机视觉的 AI 训练集，将对人工神经网络自下而上学习的进展产生深远影响。

Everyone knows the story of graduate students Sergey Brin and Larry Page's further development of the web crawler also at Stanford, and the 1998 search engine that turned the company's name “Google” into a verb for online search. The revolution in data acquisition and the very volume of data that has been progressively accumulated, such as Google ImageNet's more than 14 million labeled images serving as AI training sets for computer vision, would have a profound influence on the progress of the bottom-up learning of artificial neural networks.

随着计算机数量呈指数级增长，所有数据和信息都需要更快、更可靠的更宽带宽传输。当然，早期通过电话线传输的 9600 波特（每秒比特）是不够的，而现在卫星通信、1000 Mbps 光纤网络、2-4 GHz 频率的地面无线微波传输是当今 4G 和 5G 电话和互联网数据和信息的主要载体。

All the data and information swirling about the exponentially-increasing number of computers required the faster and more reliable transmission of broader bandwidths. Of course the early transmission over telephone lines of 9600 Baud (bits per second) was inadequate, and now satellite communications, 1000 Mbps fibre optic networks, terrestrial wireless microwave transmission with its 2–4 GHz frequencies today are the main carriers of 4G and 5G telephony and Internet data and information.

西如果源代码和技术是专有的且保密的，那么广泛、快速和便捷的计算机通信对开发新想法和创新软件的帮助就很小。自由和公开地发布和使用开源软件（OSS）进行软件开发，甚至通过众包寻找新想法，特别是利用主机编码平台的免费访问，对于人工智能的发展至关重要。

Widespread, fast, and convenient computer communication would be of little help in developing new ideas and innovative software if their source code and techniques were proprietary and kept confidential. The free and open publication and use of open source software (OSS) for software development and even crowd sourcing for new ideas particularly using the free access of host-computer coding platforms are critical to the development of artificial intelligence.

开源软件精神诞生于麻省理工学院模型铁路俱乐部，在那里，一些复杂的铁路操作的成功设计是由某人“随意修改”电路直到模型火车按计划运行而完成的。当然，好的电路被纳入了宏伟的模型中，从而可供俱乐部的所有成员使用。

The open source software ethos was born at the MIT Tech Model Railroad Club where a successful design of some complex railroad operation was completed by someone who just “hacked away” at the circuits until the model train behaved as planned. The good circuits of course were incorporated into the grand model and thereby accessible to all the members of the club.

俱乐部的兴趣从旧的铁路领域自然而然地转向了新的计算机世界。这些自由奔放的年轻人非正式地传播着完全不受限制的思想，同时开发了在 PDP-1 小型计算机上运行的第一批基本的计算机游戏。

From the old realm of railroads, the Club's interests naturally turned to the new world of computers. The free-spirited young men informally promulgated a completely unrestricted flow of ideas while they developed the first rudimentary computer games running on a PDP-1 minicomputer.

黑客精神迅速传遍了整个国家，传到了帕洛阿尔托的自制计算机俱乐部，杂志《大众电子》将黑客福音传播到全国各地，让那些有数学/电子天赋的男孩们可以尝试新技术，最终不仅苹果公司，还有微软和许多其他先驱公司，都在计算机的这种幼稚但令人兴奋的氛围中诞生。自由、开放的思想和程序交流推动了硬件和软件的开发。

The hacker spirit quickly crossed the country to Palo Alto's Homebrew Computer Club, and the magazine Popular Electronics spread the Hacker Gospel to all points in-between where boys with a mathematical/electronics bent could try their hand at the new tech, so that not only Apple, but also Microsoft and many other pioneering companies, were eventually spawned in the juvenile but heady atmosphere of computer hardware and software development spurred on by the free and open exchange of ideas and programs.

最受欢迎的自制硬件是基于 Altair 8800 家用电脑套件，运行在 1975 年 1 月《大众电子》杂志封面上的 Intel 8080 CPU 上，软件最初使用 DOS 汇编语言操作系统，后来改为更流行的 CP/M。

The most popular home-build hardware was based on the Altair 8800 home computer kit running on an Intel 8080 CPU that was featured on the January 1975 cover of Popular Electronics, and the software initially used the DOS assembly language operating system, later changing over to the more popular CP/M.

但正是黑客追随者比尔·盖茨 (Bill Gates) 痛斥了 Homebrew 兄弟，指责他们复制并分发他价值 500 美元的 BASIC 编程系统而没有向他支付任何费用，这才是真正的决断。

But it was one of the hacker acolytes, Bill Gates, who crossed the Rubicon with his lambasting of the Homebrew boys for copying and distributing his $500 BASIC programing system without paying him for it.

个人电脑的发明者史蒂夫·沃兹尼亚克 (Steve Wozniak) 一直秉持黑客精神，将自己的电脑设计免费分发给他在 Homebrew 的同事，甚至任何感兴趣的人。但在沃兹尼亚克通过电子方式模仿 AT&T 的 2600 Hz 切换音调免费拨打长途电话，破解了 AT&T 非常昂贵的长途电话后，他向 17 岁的好友史蒂夫·乔布斯 (Steve Jobs) 展示了他的“蓝盒子”，乔布斯很早就展现了自己的营销头脑，他走访了大学宿舍，那里的学生经常打电话回家和给朋友打电话，他以每台 170 美元的价格卖出了 100 多个蓝盒子，为自己和沃兹赚了不少零花钱^。1

While the inventor of the personal computer Steve Wozniak remained true to the hacker ethos in freely distributing his computer designs to his confreres at Homebrew and indeed to anyone interested. But after Wozniak hacked AT&T's very expensive long-distance calling by electronically mimicking AT&T's 2600 Hz switching tones for free long-distance calls, he demonstrated his “Blue Box” to his 17-year-old friend Steve Jobs, who early-on displayed his marketing acumen by going around to university dormitories where students made many calls home and to friends, selling more than 100 Blue Boxes for $170 each, earning substantial pocket change for himself and Woz.¹

乔布斯将苹果电脑的发明归功于他们的蓝盒子，²

Jobs credits their blue box for the invention of the Apple computer,²

如果我们不制造蓝盒子，就不会有苹果。因为我们不仅没有信心制造出并使其发挥作用……而且我们也没有能够影响世界的魔力

If we wouldn’t have made blue boxes, there would have been no Apple. Because we would have not had not only [sic] confidence that we could build something and make it work … but we also had the sense of magic that we could influence the world

但蓝盒子明显侵犯了 AT&T 的技术和商业机密，沃兹和乔布斯幸运地躲过了警方和 FBI 的调查。然而，乔布斯和盖茨后来都求助于法律来严厉谴责抄袭者，却忘记了苹果电脑后来的许多功能都是抄袭的，是由斯坦福研究所 (今天的 SRI)、施乐帕洛阿尔托研究中心 (PARC) 和伯克利软件发行部 (BSD) 的其他人发明的，而微软 Windows 的许多功能都是从苹果的 Macintosh 上抄袭而来的。

But the Blue Box clearly infringed AT&T's technology and trade secrets and Woz and Jobs were fortunate to evade the police and an FBI investigation. Both Jobs and Gates however later turned to the law as helpmate in their excoriation of copyists, conveniently forgetting the fact that many of Apple computers’ later features were copied, being invented by others at Stanford Research Institute (today SRI), Xerox Palo Alto Research Center (PARC), and the Berkeley Software Distribution (BSD), and many of Microsoft Windows’ features were simply copied from Apple's Macintosh.

然而乔布斯的愿望是建立一家经久不衰的公司，创造创新型新产品并满足需求（其中一些甚至连消费者自己都不知道），从而提供新的效用，如果使用得当，将造福社会（例如，手机使叫车服务成为可能），但苹果似乎永远在法庭上指控非常简单的技术侵犯版权和专利（例如，iPhone 的曲面边缘和比例），以期赶走竞争对手。

Jobs’ desideratum however was to establish an enduring company that would create innovative new products and supply demands (some of which even consumers themselves were unaware), and thus provide new utility that would benefit society if properly used (for example, the mobile phone makes ride-hailing possible), but Apple seemed to be forever in court charging copyright and patent infringement of very simple technology (for example the curved iPhone edges and proportions) in an effort to drive out competitors.

盖茨缺乏创新精神，但更善于投机取巧，他只是利用 IBM 和 PC 克隆产品的近乎垄断地位，从操作系统和应用软件许可中获取巨额寻租利润。永无止境的Windows新版本反映了盖茨专注于一项商业战略，即利用消费者对新功能（不一定有用）和最新科技时尚产品的渴望^。3

The less innovative but more opportunistic Gates was simply riding on IBM and the PC clones’ near monopoly to make exorbitant rent-seeking profits from his operating system and applications software licenses. The never-ending new Windows versions reflect Gates’ concentration on a commercial strategy that exploited consumers’ desire to have (not necessarily useful) new features and the latest tech-fashion products.³

盖茨凭借其个人电脑操作系统垄断积累了大量财富之后，他晚年精心选择了一些值得资助的事业，虽然这值得称赞，但在某些人看来，这不过是他对自己过去商业违规行为良心的忏悔，或许是为了购买一枚通往不应得的天堂的门票。

After amassing his fortune from his personal computer operating system monopoly, Gates’ late-blooming philanthropy for well-selected worthy causes, although laudable, appeared to some as conscience-stricken amends for past commercial transgressions, perhaps being purchases of wishful tickets to an undeserved Heaven.

微软表面上已经重塑为一家更加开放、更具社会责任感的公司，它公布并授权了神圣的操作系统源代码，并承诺在新的首席执行官萨蒂亚·纳德拉的领导下更加合作。但这个终极商业掠食者真的能改变自己的本性吗？

Microsoft ostensibly has been re-engineered as a more open and socially responsible company with the publication and licensing of its holy operating system source code and a promise to be more cooperative under direction of the new CEO Satya Nadella. But can the ultimate commercial predator really change its spots?

幸运的是，对于人工智能的发展来说，软件得到了开放源代码促进会（OSI）黑客精神重生的祝福，OSI 是一个提倡自由使用和公开发布的非盈利组织。通过主机编码平台分发源代码，用于参与新软件的开发。

Fortunately for the development of artificial intelligence, software has been blessed by the rebirth of the hacker spirit in the Open Source Initiative (OSI), a non-profit organization promoting free use and openly distributed source code for participation in new software development through host-computer coding platforms.

然而，企业开源却在 AT&T 这个知识产权的坚定保护者身上不合时宜地诞生。原因是，在 20 世纪 60 年代之前，AT&T 被司法部根据一项同意令指定为美国电话系统的官方批准垄断企业，以确保兼容的公用事业服务，事实上，几代人以来，笨重的黑色拨号电话是唯一可用的电话型号，而所有电话、交换机、中继站和固定电话都是由 AT&T 的制造子公司西部电气生产的。为了防止 AT&T 垄断地位进一步扩大，司法部禁止 AT&T 从事电话通信以外的任何活动，特别是在蓬勃发展的计算机新领域。

Corporate open source however was incongruously hatched at AT&T, a fierce protector of its intellectual property rights. The reason is that before the 1960s, AT&T was designated as an officially sanctioned monopoly of America's telephone system under a Consent Decree by the Department of Justice to ensure compatible public utility services, and indeed for generations the stodgy black dial phone was the only telephone model available, while all the phones, switchboards, relay stations, and land lines were produced by AT&T's manufacturing subsidiary Western Electric. To prevent the further expansion of AT&T's monopoly, the Justice Department prohibited AT&T from any activities outside of telephone communications, and particularly in the burgeoning new field of computers.

因此，在 20 世纪 70 年代，肯·汤普森在贝尔实验室开发的 UNIX 操作系统及其用于计算机间通信的衍生产品的源代码根据通用公共许可证(GPL) 免费分发给大学，商业使用费用为 20,000 美元。UNIX 迅速成为事实上的标准科学和工程通信链路，服务于大学、研究机构、技术公司和政府机构。

And so in the 1970s the source code for Ken Thompson's UNIX operating system and its derivatives for inter-computer communication developed at Bell Labs was freely distributed to universities under a General Public License (GPL), and for a nominal $20,000 for commercial use. UNIX quickly became the de facto standard science and engineering communication link serving universities, research institutions, technology companies, and government agencies.

然而，在 1983 年政府强制 AT&T 解散为地区性“小贝尔”公司，以及伟大的贝尔实验室惨遭解散之后，AT&T 终于摆脱了反垄断同意令，迅速回归商业本源，认为 UNIX 是专有的，使用 UNIX 需缴纳高达 25 万美元的巨额许可费。其源代码严格保密并受版权保护，副本的分发仅以目标代码形式进行，虽然不是人类可读的，但也受版权保护^。4

However, after the government-mandated dissolution of AT&T in 1983 into regional “Baby Bells”, and the grievous dissolution of the great Bell Labs, at last free from the antitrust Consent Decree, AT&T quickly reverted to its commercial roots, deeming UNIX proprietary and its use subject to substantial licensing fees up to $250,000. Its source code was strictly confidential and protected by copyright, the distribution of copies were in object code only, and although not human-readable, also protected by copyright.⁴

因此，尽管 AT&T 催生了通用公共许可证的概念，但它却通过建立繁琐的专利使用费许可制度（微软等公司随后也采用了该制度）以及为侵权诉讼提供法律基础（苹果等公司将积极提起该诉讼）而终结了商业开源软件的概念^。5

And so, although birthing the concept of a General Public License, AT&T turned around and terminated the idea of commercial open source software by establishing the onerous royalty-bearing licensing regime subsequently employed by, among others, Microsoft, and the legal basis for infringement suits that would be aggressively pursued by, in particular, Apple.⁵

AT&T UNIX 现已封闭的系统让快速发展的计算机科学学科的年轻成员感到不满，而 BSD 则创造了许多竞争性替代品，但特别是公认的计算机科学天才理查德·斯托曼 (Richard Stallman) 主动开发了一种竞争性的计算机间操作系统，他称之为“GNU”，这是一个递归缩写，即“GNU's Not UNIX”，其源代码是公开的、免费的，并且可以自由分发，并包含一个开发工具包，以鼓励参与开放操作系统及其实施和应用程序的进一步开发。

The AT&T UNIX now closed system rankled the young members of the fast-developing academic discipline of computer science, and BSD created many competitive alternatives, but in particular the acknowledged computer science genius Richard Stallman took it upon himself to develop a competing inter-computer operating system he called “GNU”, a recursive acronym, “GNU's Not UNIX”, the source code of which was public, free, and freely distributable, and included a developmental toolkit to encourage participation in further development of the open operating system and its implementation and applications.

斯托曼骑着 GNU 这匹开放的角马，穿过计算机科学系的大厅和全球黑客的家园，热情的斯托曼向所有人提供可自由使用和分发的开源软件，同时严厉批评苹果和微软拒绝公众获取源代码的行为，称其为真正的“反人类罪”，将扼杀新兴计算机软件学科及其相关产业的发展。

Mounted on the open range wildebeest GNU trampling through the halls of computer science departments and the homes of hackers worldwide, the wild-eyed Stallman offered open source software for all to freely use and distribute, all the while excoriating Apple and Microsoft's denials of public access to source code as veritable “crimes against humanity” that would stifle the growth of the new computer software discipline and its related industries.

不知所措的苹果和微软实际上用自己的垄断取代了 AT&T 和 IBM 的垄断，并且忙于通过繁重的许可计划（微软）和强有力的专利和软件版权执行（苹果）来限制个人计算机操作系统和应用软件的交易。

Apple and Microsoft, nonplussed, in effect replaced AT&T and IBM's monopolies with their own, and were busily restraining the trade for personal computer operating systems and applications software with onerous licensing programs (Microsoft) and vigorous enforcement of patents and software copyright (Apple).

讽刺的是，最早的宽松主机编码平台之一 BSD 于 1992 年被 AT&T 起诉侵犯 UNIX 版权（导致 BSD 的进一步开发推迟了两年），体现了微软和苹果对版权执行的热情，而微软后来在 Windows 2000 中玩世不恭地使用了 BSD 编写的代码，而苹果的 macOS 和 IOS 操作系统主要基于FreeBSD。看来，在计算机软件的商业化世界中，鱼与熊掌可以兼得^。6

It is of utmost irony that one of the first permissive host-computer coding platforms, BSD, was sued by AT&T for copyright infringement of UNIX in 1992 (delaying BSD's further development for two years) exemplifying the copyright enforcement zeal of Microsoft and Apple, while Microsoft later cynically used BSD-produced code in Windows 2000 and Apple's macOS and IOS operating systems were largely based on FreeBSD. It seems that in the commercialization world of computer software one can have one's cake and eat it too.⁶

在与秘密和专有软件的斗争中，斯托曼的征战在遥远的芬兰的一次演讲中找到了志同道合的人。受到斯托曼演讲的启发，赫尔辛基大学研究生 Linus Torvalds 使用 GNU 工具包开发了同名的Linux，作为个人电脑的开源竞争操作系统。1991 年，他根据 GPL 在网上发布了源代码，吸引了许多年轻黑客，他们不仅将其用作微软操作系统的替代品，还邀请他们改进它并基于它开发新的实用程序和应用程序，这是众包的早期实例。

In his fight against secret and proprietary software, Stallman's crusade found a kindred spirit during a speech in far-away Finland. Inspired by his talk, the University of Helsinki grad student Linus Torvalds, using the GNU toolkit, developed the eponymous Linux as an open source competing operating system for personal computers. He published the source code online in 1991 under a GPL, attracting many young hackers to not only use it as a substitute for Microsoft's OS, but also inviting them to improve it and develop new utilities and application programs based on it in an early instance of crowdsourcing.

Linux 将计算机操作系统和应用软件的开发从微软秘密源代码的束缚中解放出来，为新兴科技公司提供了一个操作系统平台，让他们可以在此平台上开发自己的新软件。苹果仍然是封闭系统、高价专有硬件和软件的堡垒，尽管其产品有计划淘汰和营销花招，但凭借如今必不可少的新产品舞台表演，每^款新产品都成为高科技时尚达人的宠儿。7

Linux liberated the development of computer operating systems and application software from the tyranny of Microsoft's secret source code, providing new tech start-ups an operating system platform on which to develop their own new software. Apple has remained a bastion of closed-system, overpriced proprietary hardware and software that despite its products’ planned obsolescence and marketing subterfuges, by means of his now de rigueur new product stage performances, each new product became the darling of the high-tech fashionista.⁷

尽管如此，当全世界都在哀悼这位科技偶像 2011 年的逝世时，据报道，当被问及他对开源信条的反应时，斯托曼说：“我并不高兴他去世，但我很高兴他走了。” ⁸

Notwithstanding, while the world mourned the death of the tech icon in 2011, when asked for his reaction, ever-true to his open source creed, Stallman was reported to have said, “I’m not happy that he died, but I am glad that he is gone”.⁸

事实是，苹果公司的史蒂夫·乔布斯和微软公司的比尔·盖茨的严酷商业专制与理查德·斯托曼和林纳斯·托瓦兹的梦幻理想主义之间的冲突，将在人工智能发展中粗俗的寻租行为和理想主义的自由开放软件之间的妥协中找到共同点。

It has come to pass that the conflict between the harsh commercial despotism of Apple's Steve Jobs and Microsoft's Bill Gates against the dreamy idealism of Richard Stallman and Linus Torvalds would find common ground in a compromise between crass rent-seeking and idealistic free and open software in the development of artificial intelligence.

可以理解的是，激励男孩自由炫耀其编程技能的名声可能不足以满足需要养家糊口的男人。该领域的创造力和辛勤工作无疑应该得到相应的报酬，但另一方面，该领域的信息和思想的自由和开放交流对其发展必不可少，而对于影响深远的人工智能科学和技术来说，这一点至关重要。

It can be understood that the notoriety that motivates a boy to freely show off his coding skills may not suffice for the man who has to feed a family. The creativity and hard work in his field no doubt deserve proportionate remuneration, but on the other hand, the free and open exchange of information and ideas in that field are necessary to its development, and now critically so for the far-reaching science and technology of artificial intelligence.

因此，加州大学的科技理想主义者们，遵循着伯克利的精髓，与开明工程的堡垒麻省理工学院 (MIT) 设计了 ​​GPL 的衍生产品——宽容软件许可证(PSL)，并建立了BSD和MIT 许可证制度，提倡新软件的开源开发，但出于对企业家精神的认可，允许利用新开发的商业软件，而不需要发布源代码。

So the tech idealists at the University of California, in conformance with the Berkeley quintessence, together with kindred spirits at the citadel of enlightened engineering MIT, devised a GPL derivative, the Permissive Software License (PSL), and established the BSD and MIT License regimes that advocated the open source development of new software, but with a nod to entrepreneurship, permitted the exploitation of newly-developed commercial software that did not require publication of the source code.

因此，一个可能带来丰厚利润的软件产品可以作为知识产权受到保护，从而奖励其创造者专有权利，但该产品的软件起源是开源的，任何人都可以免费使用。通过这种方式，商业化可以鼓励新想法，但实现想法所需的工具将是免费的。例如，C++、Java、Python语言，以及Wolfram、Matlab和Octave上提供的固定数值分析和线性代数程序，以及众多免费工具、工具包和应用程序以及在线编程教程和主机源代码平台（如RedHat和Github）都可用于帮助指导和实现新产品。这种发展制度对新人工智能算法的创造起到了重要作用^。9

So a potentially lucrative software product could be protected as intellectual property, rewarding its creator with exclusive rights, but the software genesis of that product was open source, free for anyone to use. In this way, commercialization could encourage new ideas, but the tools necessary for manifesting the idea would be free. For example, the languages C++, Java, Python, and canned numerical analysis and linear algebra programs such as available on Wolfram, Matlab and Octave, plus numerous free tools, toolkits, and applications programs together with online programming tutorials and host-computer source code platforms such as RedHat and Github are all available to help guide and realize the new product. This type of a developmental regime was instrumental in the creation of new artificial intelligence algorithms.⁹

例如，在抗击新冠病毒及其变体的斗争中，哈佛医学院蛋白质折叠算法源代码在 GitHub 上公开；百度的Linearfold mRNA 蛋白质折叠算法、华盛顿大学（圣路易斯）Folding@Home开源个人计算机链接以百亿亿次浮点运算（10 ¹⁸次操作）的速度运行，用于众包蛋白质折叠开发；IBM、谷歌、亚马逊和微软都已提供其计算机能力来研究针对新冠病毒的疫苗。英特尔与阿贡国家实验室合作的Aurora超级计算机项目也将参与蛋白质折叠计算，以寻找用于治疗和疫苗的抗病毒药物。

For example, in the fight against the corona virus and its variants, the Harvard Medical School protein folding algorithm source code was publicly available on GitHub; Baidu's Linearfold mRNA protein folding algorithm, the Washington University (St. Louis) Folding@Home open source personal computers link that ran at exaflop (10¹⁸ ops) capacity for crowd-sourced protein folding development, and IBM, Google, Amazon, and Microsoft have all made their computer power available to research vaccines against the corona virus. The Intel-Argonne National Laboratory cooperative Aurora supercomputer project also will take part in protein folding calculations to find anti-viral drugs for treatment and vaccines.

疫苗研发和生产专利权豁免的提议也是开源趋势的一个指标。在疫情肆虐的全球背景下，世界正在向开源迈进，这是令人欣慰的；希望疫情消退后，开源仍是人工智能发展的基础。

The proposal of the waiving of patent rights for vaccine development and manufacture is also an indicator of the trend towards open source. It is gratifying that the world is progressing to open source in the face of an overwhelming global pandemic; let us hope that open source remains the basis for the development of artificial intelligence after the pandemic withers away.

三从上到下

III From Top to Bottom

我1956 年，在达特茅斯学院首次举办的人工智能夏季研究项目中，人工智能先驱约翰·麦卡锡和马文·明斯基在一份拨款提案中提出了他们的目标是开发纯粹自上而下的人工智能机器，¹

In 1956, at the inaugural Dartmouth Summer Research Project on Artificial Intelligence, the AI pioneers John McCarthy and Marvin Minsky set out their goal of a pure top-down artificial intelligence machine in a grant proposal,¹

这项研究基于这样的猜想：学习的每一个方面或智力的任何其他特征原则上都可以被如此精确地描述，以至于机器可以模拟它

The study is to proceed on the basis of the conjecture that every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it

他们的猜想在哲学上基于笛卡尔心身问题的一元论；也就是说，抽象思维和物理大脑是不可分离的，因此思维可以由物理机器产生^。2

Their conjecture was philosophically based on the monism of Descartes’ mind-body problem; that is, an abstract thought and the physical brain are not separable, and thus a thought could be produced by a physical machine.²

两位与会者，艾伦·纽厄尔 (Allen Newell) 和赫伯特·西蒙 (Herbert Simon)，选择了一项他们认为可以最终证明该猜想的任务：一台可以证明数学定理的机器^。3

Two attendees at the conference, Allen Newell and Herbert Simon, picked a task that they believed would be an ultimate proof of the conjecture: a machine that could prove mathematical theorems.³

根据阿尔弗雷德·诺思·怀特黑德和伯特兰·罗素于 1913 年在其划时代的三卷本著作《数学原理》中提出的符号逻辑规则，使用一组符号来表示同义反复 比如“所有未婚男人都是单身汉”， “如果A意味着B，且B意味着C，则A意味着C ”这样的推论，以及唯一性的数学概念（$\exists ！$）和完整性（对于每一个$\mathrm{\Gamma }\models \mathrm{\phi }$也确实如此$\mathrm{\Gamma }⊢\mathrm{\phi }$）。

From the rules of symbolic logic as set forth in 1913 by Alfred North Whitehead and Bertrand Russell in their epochal three-volume tome Principia Mathematica, a set of symbols is used to represent tautologies such as “All unmarried men are bachelors”, inferences such as “if A implies B, and B implies C, then A implies C”, and the mathematical concepts of uniqueness ($\exists !$) and completeness (for every $\mathrm{\Gamma }\models \mathrm{\phi }$ it is also true that $\mathrm{\Gamma }⊢\mathrm{\phi }$).

逻辑理论家使用创新的信息处理语言（IPL）（列表处理器（LISP）人工智能语言的前身）将单词和短语转换为二进制编码的符号，并通过在树搜索中比较和匹配符号串，其中根是假设，每个分支都是基于符号逻辑的推论，目标是树的一个树枝；证明是从根到分支再到树枝的轨迹。

The Logic Theorist, using the innovative Information Processing Language (IPL), a forerunner of the List Processor (LISP) artificial intelligence language) converted words and phrases into binary-coded symbols, and by comparing and matching symbol strings in a tree search where the root is the hypothesis, each branch is a deduction founded on symbolic logic, and the objective is at a twig of the tree; the proof is the trajectory from root through branch to twig.

在达到目标的过程中，人们可以做出许多不同的选择和组合。人们可以逐一尝试所有可能性，检查结果，如果需要，可以回溯尝试下一个可能性。即使是对于一些数学基本定理的证明和棋盘游戏等受限领域的问题，这种穷举搜索方法也会遇到需要当今超级计算机来计算的组合可能性爆炸。

There are many different choices and combinations that one can take along the way to reach the goal. One can try all the possibilities one-by-one, checking the result, and if wanting, backtrack to try the next possibility. Even for restricted domain problems such as the proof of some basic theorems of mathematics and the playing of board games, this exhaustive search method would encounter a combinatorial explosion of possibilities requiring today's supercomputers to compute.

优秀的数学家当然不会仅仅通过反复试验的穷举搜索来做数学题，人类的国际象棋和围棋选手也不会以如此平淡无奇的方式下棋，而是利用知识、逻辑和启发式方法来减少选择数量，制定策略并积累经验。

Good mathematicians of course do not do mathematics solely by trial-and-error exhaustive search, and human chess and Go players also do not play in such a pedestrian manner, rather they use knowledge, logic, and heuristics to reduce the number of choices, formulate strategies, and gain experience.

自上而下的专家系统支持者的想法是，对基本操作进行硬连线，收集最佳实践者的知识和启发式方法，添加方法-目的分析以反馈流程是否在正确轨道上的信息，然后从期望的结果开始逆向工作，选择最佳的成功路径。

The top-down proponents’ idea for expert systems was to hard-wire the fundamental operations, collect the knowledge and heuristics of the best practitioners, add means-end analysis to feedback information that a process was on the right track, and then working backwards from the desired result, pick the best paths to success.

总之，这被称为爬山，因为登山者向上而不是向下的步伐通常更有可能有助于实现到达山顶的目标。然而，反映任何努力的复杂性，向下的步伐可能会导致无法预见的较低水平的绳索通道到达山顶，因此爬山轨迹方法显然不是绝对的；数学中的例子可能是矛盾证明（tertium non datur），游戏中的例子可能^是国际象棋中的后牺牲以及围棋中的手拔和先手。4

Altogether this was called hill-climbing because a mountain-climber's step up rather than down is generally more likely to contribute to the goal of reaching the summit. However, reflecting the complexity of any endeavor, a step down might lead to an unforeseen lower level roped passage to the top, so the hill-climbing trajectory approach is obviously not absolute; examples in mathematics might be proof by contradiction (tertium non datur), and in games, queen sacrifice in chess and tenuki and sente in Go.⁴

逻辑理论家成功地证明了《自然哲学的数学原理》定理，甚至证明了与《自然哲学的数学原理》证明本身不同的方式，这让伯特兰·罗素本人感到高兴。

The Logic Theorist succeeded in proving Principia theorems, even in ways different from the Principia proofs themselves, delighting Bertrand Russell himself.

从这一成功经验来看，自上而下的专家系统可以将大问题分解为多个较小的子问题，然后按照“如果-那么”程序步骤依次解决每个子问题，并将所有子问题集成到一个核心推理引擎中，原则上该引擎可以解决任何问题。

From this success, top-down expert systems could break a big problem into smaller sub-problems, tackling each in turn by if-then program steps, and integrating all the sub-problems into a core inference engine that in principle could solve any problem.

例如，如果问题是赢得一场美式足球比赛，那么每一系列进攻都是一个子问题，传统训练的主教练会推理：如果你在球场的另一端，如果是第四次进攻并且还剩 8 码，那么就弃踢。然而，比赛策略和人员可能会决定其他情况；例如，你有一个好的假弃踢战术，一个可以跑动或传球的弃踢手，以及一个被认为保守的教练，这会导致意外。专家系统可以客观地考虑其他选择，尤其是因为它可以忽略未经证实的教练说教并接受风险假设（短期内输掉比赛，长期内被解雇）。

For example, if the problem is to win an American football match, each series of downs is a sub-problem, a traditionally-trained head coach would reason: if you are in your end of the field, and if it is fourth down and 8 yards to go, then punt. However, game strategy and personnel might dictate otherwise; for instance, you have a good fake-punt play, a punter who can run or pass, and a coach whose perceived conservatism would result in surprise. The expert system could objectively take into consideration other options not the least because it can disregard unsubstantiated coaching homilies and accept the assumption of risk (short-time losing the game, and long-term getting fired).

成功解决融入整个比赛的子问题将更有可能取得胜利，因此专家系统指导推理引擎由于其逻辑组织的方法，应该比人类主教练表现更好。

Success in tackling the sub-problems integrated into the total match will more likely result in victory, so an expert system coaching inference engine, due to its logically-organized approach, should perform better than a human head coach.

自上而下的专家系统的最终测试是深蓝。棋局的每个状态都呈现出一种特定的棋子排列，玩家面对的是一组必须评估的合法棋步的静态数组。评估函数用于判断某一步是否可能对玩家有利；例如，某一步是否捕获了对手的威胁性重棋子。使用alpha-beta剪枝的极小极大算法来减少分支数量，并且树搜索的逐步深化通过在树中较高（较早）的级别做出决策来加快评估速度。

The ultimate test of the top-down expert system was Deep Blue. Each state of a chess game presents a particular arrangement of the pieces with a player faced with a static array of of legal chess moves that must be evaluated. An evaluation function is used to see if a particular move is probably beneficial to the player; for example, if a move captures an opponent's threatening heavy piece. A minimax algorithm with alpha-beta pruning to reduce the number of branches, and a progressive deepening of the tree search speeds up the evaluations by making decisions at higher (earlier) levels in the tree.

Deep Blue 的极小极大算法使用了一种决策树的数据结构，该决策树具有一个位于顶部的根节点，以及从该节点向下延伸的子节点，分支因子 b是连接到该节点的子节点的数量，树的深度d大致是从根节点到最远的叶节点的决策节点数。

Deep Blue's minimax used a data structure decision tree having nodes with a root node at the top, and children descending from the nodes, and a branching factor b that is the number of children connected to the node, and the depth of the tree d is roughly the number of nodes of decision-making from the root down to the farthest leaf node.

在典型的国际象棋游戏中，深度为d = 100，如果b = 3（不是一棵很深的树），则叶节点（决策）的数量为b ^d = 3 ^100，这意味着根据数学家 Claude Shannon 的估计，一场游戏中将进行大约 10 ^{120 次}静态评估。七级层数越多，玩家就越难成为普通玩家，而成为大师则至少需要 15 层。

In a typical chess game, a depth of d = 100 and if b = 3 (not a very deep tree), the number of leaf nodes (decisions) is given by b^d = 3¹⁰⁰ which means that as estimated by the mathematician Claude Shannon there will be about 10¹²⁰ static evaluations to be made in a game. A level of seven layers makes a mediocre player and at least 15 layers are required for a Grandmaster.

即使以每秒 2 亿次评估的速度，穷举搜索也是不可行的，因此搜索树必须通过上下极小化和并行处理计算进行alpha-beta剪枝，并且能够使用扩展的爆炸搜索执行不均匀的树开发来处理特殊遭遇，例如王车易位或脆弱的皇后。

Even at a rate of 200 million/second evaluations, exhaustive searches would not be feasible, so the search tree must be alpha-beta pruned with up-and-down minimaxing with the calculations parallel-processed, and capable of performing uneven tree development using extended blow-up searches to take care of special encounters, such as castling or a vulnerable queen.

Alpha-beta 剪枝是一种基于极小极大理论的方法，通过从树的根部到树枝再到树叶的上下搜索来消除无效路线，以找到到达目标节点的最佳路线，这样可以消除（剪枝）效率较低的路线，从而减少组合可能性。

Alpha-beta pruning is a method based on the minimax theory of eliminating unproductive routes by going up and down from the root through branches to leaves in a tree search to find the optimum route for reaching the goal node, and as such the less effective routes can be eliminated (pruned), and thus reduces the combinatorial possibilities.

Alpha是最大化器已探索的最佳路线，而beta是最小化器已探索的最佳路线，可能的路线如下图所示的简化搜索树所示。

Alpha is the best already-explored route for the maximizer and beta is the best already-explored route for the minimizer, the possible routes are shown in the simplified search tree shown in the figure below.

从路线的最坏情况值开始，对于最大化器来说，它是 −∞，对于最小化器来说，它是 +∞。一开始，除了搜索树的叶节点之外没有初始值，这些叶节点在进行任何新移动之前评估最终位置的“优劣”。这些叶节点静态评估可以有多种选择，国际象棋的一个简单示例可能是赢得对手的重棋子，这样玩家的重棋子在游戏的那一刻就会更大。

Starting with the worst case values for a route, for the maximizer it is −∞ and for the minimizer it is +∞. At the outset, there are no initial values except at the leaf nodes of the search tree which evaluate the “goodness” of a final position before any new moves are made. These leaf node static evaluations can be variously chosen, a simple example for chess could be winning an opponent's heavy piece such that a player's heavy pieces will be greater at that point in the game.

从搜索树的根开始，玩家沿着分支逐个比较值，这些值最初总是 +/–∞，不允许进行任何评估，直到到达叶节点，此时可以进行比较。然后逐个向后穿过所有分支回到根，当有一个更好的值（对于最大化者来说更正，对于最小化者来说负值较小）时，该分支将是最佳选择，所有较差的分支选择都可以丢弃。搜索树的这种“修剪”揭示了“噪音”最少的路线，所有其他分支都可以丢弃^。5

Starting from the root of the search tree, a player goes along the branches one-by-one comparing values, which at first are always +/–∞ allowing no evaluations until a leaf node is reached, at which point a comparison can be made. Then going backwards through all the branches one-by-one back towards the root, when there is a value that is better (more positive for the maximizer and less negative for the minimizer), that branch will be the best choice and all the worse branch choices can be discarded. This “pruning” of the search tree reveals the routes with the least “noise”, and all the other branches may be discarded.⁵

尽管被称为“逐步深化”，但迭代深化深度优先搜索(IDDFS) 在实践中会通过对可能有益的分支进行早期迭代（例如因为它是基于某些国际象棋启发式方法的好举动）来减少最终的树搜索深度，直到在该分支中找到一个好的节点。

Despite being called “progressive deepening” the iterative deepening depth-first search (IDDFS) in practice reduces the ultimate tree search depth by earlier iteration of a probably beneficial branch (for example because it is a good move based on some chess heuristic) until a good node is found in that branch.

深蓝通过使用充当评估器的硬连线移动生成器进行树搜索，根据大师对已发布比赛中的叶节点值的确定进行 alpha-beta 剪枝。开局书和残局由深蓝的大师顾问提供并存储以供随机访问。

Deep Blue played by doing the tree search using hardwired move generators acting as evaluators that alpha-beta pruned based on a Grandmaster's determination of leaf node values in published matches. Opening books and endgames were provided by Deep Blue's Grandmaster advisors and stored for random access.

评估函数的一个例子是众所周知的策略，即车和象可以有利地放置在队列上或队列附近，这样可以通过移除队列上的兵（通常通过吃掉兵）来提前“打开队列”，从而对对手的重棋施加远程和长期压力。当然，不能过早打开队列，让对手注意到并进行干扰或挑战。相反，车和象应该设置在“可能打开”的队列上，玩家应该等待合适的时机打开队列。

An example of an evaluator function is the well-known tactic that rooks and bishops could be advantageously placed on or near files where there is an option of early “opening up the files” by removing the pawns on the files (typically by pawn capture) and thereby exerting long-range and long-term pressure on the opponent's heavy pieces. The file of course must not be opened prematurely allowing the opponent to notice and disrupt or challenge. The rooks and bishops rather should be set up on a “potentially open” file and the player should wait for an opportune moment to open the file.

至于整体战略和游戏中的反应，必须识别棋盘模式。一项以冠军棋手为受试者的实验发现，他们几乎可以立即记住合理的棋盘布局，但无法记住不合理的布局，因此得出结论，职业棋手是通过对棋盘布局的模式识别来下棋的棋盘上的棋子，通过经验、启发法和技巧，能够对逻辑棋盘做出合理的反应。比赛中棋手一脸困惑，这肯定表明棋盘的布局不合理，违背了他们的经验和/或逻辑。对于计算机来说，它的程序可能会被“无法识别”的模式弄得混乱，从而导致一些奇怪的反应。

As for overall strategy and in-game responses, board patterns must be recognized. An experiment of champion chess players as subjects found that they could almost immediately memorize rational board layouts, but could not memorize irrational layouts, so it was concluded that professional chess players play by the pattern recognition of the disposition of the pieces on a board, and through experience, heuristics, and skill, can rationally respond to a logical board. A face screwed-up in confusion during a match is a sure sign of an irrational board disposition contrary to their experience and/or logic. For the computer, its program may be discombobulated by an “unrecognized” pattern, causing some weird responses.

例如，当深蓝的前身深思（Deep Thought） ——第一台在正式比赛中击败国际象棋大师的计算机——面对右图所示的不太可能出现的假设棋盘布局时，人类棋手会清楚地看到黑棋拥有两个车和一个象的棋子，具有巨大优势，而白棋只有王和兵，但这些兵排列成一条严密的防线。只需将白王移到兵线后面，就可以轻松打成平局。但因为这样可以获得物质利益，又没有直接的人身威胁，深思吃掉^了黑车和兵，从而摧毁了兵的防线，最终失败是不可避免的。6

For example, when Deep Blue's predecessor, Deep Thought, the first computer to defeat a Grandmaster in a sanctioned game, was presented with the admittedly not likely to encounter hypothetical board layout shown in the figure at right, it would be clear to a human player that black has an enormous advantage in pieces with two rooks and a bishop, while white has only a king and pawns, but those pawns are arrayed in an airtight defensive line. A draw could easily be achieved by just moving the white king around behind the line of pawns. But because it was available for material gain with no immediate personal threat, Deep Thought took the black rook with its pawn, and in doing so destroyed the line of pawns defense, resulting in an inevitable defeat.⁶

即使是普通人类棋手，看到棋盘上的图案后也不会犯这样的错误，但深思显然没有意识到这种不寻常的棋盘图案，而是自上而下地被编程来吃掉棋子并试图将死黑王。深思做了它该做的事，而专家系统在这种情况下只不过是一个笨手笨脚的业余爱好者，这证明了虽然“专家”也可能很愚蠢。

Even a pedestrian human player, having seen the pattern on the board, would not have made that mistake, but Deep Thought apparently did not recognize the unusual board pattern and was top-down programmed to capture pieces and attempt to checkmate black's king. Deep Thought did what it did, and the expert system in this case was no more than a bungling amateur, proving that although “expert” it could also be stupid.

深蓝拥有更大的内存、更快的处理器和更多的下棋启发式方法，可以通过编程避免“深思”的天真，但是，不寻常或非理性的玩法可能会混淆计算机的想法逐渐萌芽，卡斯帕罗夫就相信这是战胜机器的关键。

Deep Blue, with more memory, faster processors, and more chess-playing heuristics, could avoid Deep Thought's naïveté by programming, but the idea that unusual or irrational plays could confuse the computer germinated such that Kasparov for one, believed that this was the key to victory over a machine.

和所有伟大的冠军一样，卡斯帕罗夫在比赛前刻苦研究对手，以发现对手的下棋倾向和弱点。从与其他国际象棋计算机的赛前训练中，卡斯帕罗夫显然意识到由于计算机对好棋步的搜索非常彻底，直接的比赛很难取胜，因此设计了一种“反计算机”策略，故意走次优步，让深蓝无法识别，就像深思和奇怪的兵线防御一样，他认为这是国际象棋计算机可以利用的弱点。

Like all great champions, Kasparov assiduously studied his opponent before-match to find playing proclivities and weaknesses. From his pre-match training with other chess computers, Kasparov evidently realized that because of the sheer thoroughness of search for good moves that a computer can bring to bear, a straight-up match would be difficult to win, and so devised an “anti-computer” strategy of deliberately playing suboptimal moves that Deep Blue would not recognize, just like Deep Thought and the strange pawn-line defense, he thought that that was the chess computer's weakness that could be exploited.

因此，在第一局中，即使白棋占优，卡斯帕罗夫也放弃了常规开局，即使深蓝的黑象潜在对角线明显（如右图所示），他的重棋也从未离开过自己的半盘。前九步棋，棋子都处于封闭状态，位置高度紧张，但在令人不安的10.e3步中，卡斯帕罗夫证实了他次优的后退策略，因为正常步数是10.e4，可以交换兵。

Therefore in Game 1 even with white advantage, Kasparov abandoned normal openings, and his heavy pieces never left his own half of the board even when Deep Blue's black bishop potential diagonal file was evident as shown in the figure at right. For the first nine moves, the pieces were closed and highly positional, but in a disconcerting 10.e3 move, Kasparov confirmed his suboptimal laying-back strategy, as a normal move would be a 10.e4 offering a pawn exchange.

然而，深蓝并没有利用这个次优的着法来获得主动权，因为在这个例子中，它的评估函数的自动调整增加了某些着法的权重，但在极端情况下，权重达到了最大，这种饱和意味着深蓝不再区分非常糟糕的局面和更糟糕的局面。卡斯帕罗夫相信他的策略是有效的。

Deep Blue, however, did not capitalize on this suboptimal move to gain the initiative, because in this instance, its automatic tuning of the evaluation function had increased the weighting for certain types of moves, but in extreme cases the maximum weight was reached, and this saturation meant that Deep Blue no longer distinguished a very bad position from an even worse position. Kasparov believed his strategy was working.

饱和漏洞后来被发现和纠正，但经过几次有问题的举动后，深蓝输掉了第一局，但知道自己为什么会输，而卡斯帕罗夫在开场的小规模战斗中只获得了白棋的预期胜利，但在获胜的过程中，他对次优退棋策略的信念得到了加强。

The saturation bug was found and corrected later, but after a few more questionable moves, Deep Blue lost Game 1, but knew why it lost, and Kasparov only gained an expected white victory in the opening skirmish, but in winning, his belief in his suboptimal move lay-back strategy was reinforced.

在第二局比赛中，深蓝积极应对卡斯帕罗夫的后撤，利用车和象可能打开的线和对角线将卡斯帕罗夫的重棋子压制在后排，从而取得进攻并最终获胜，卡斯帕罗夫的反计算机策略因此土崩瓦解。鉴于他在第一局比赛中取得的成功，卡斯帕罗夫认为，如果没有人类操作员识别出次优的走法并在比赛中改变战术，深蓝无法适应并反击他的策略。他在比赛结束后抱怨道：

In Game 2, Kasparov's anti-computer strategy fell apart when Deep Blue, affirmatively responding to the lay-back, pinned down Kasparov's heavy pieces to his back rank utilizing rook and bishop potentially open files and diagonals, taking the offensive and final victory. In light of his success in Game 1, Kasparov did not believe that Deep Blue could adapt and counter his strategy without human operators recognizing the sub-optimal moves and changing tactics in-game. He complained after the match,

你知道，（反计算机策略）曾经发挥作用，但突然间它就失效了——深蓝突然找到了一种方法来打破兵链，并在非常非常方便的情况下开始对抗。

You know, [the anti-computer strategy] was working, but suddenly it stopped working – suddenly Deep Blue found a way just to break the pawn chains and start a confrontation in a very, very convenient situation.

深蓝在第二局的最后一步棋Ra6被评论员视为“非常可疑但非常出色的一步棋”，这足以令人震惊地以深蓝的满分结束了这场比赛。卡斯帕罗夫的怀疑和作弊指控无疑影响了他的发挥，并且可能是他在第二局中错失实质性平局机会的因素，正如他的助手在赛后分析中所指出的那样，他的黑棋因此错失了获得关键半分的机会。

Deep Blue's last move in Game 2, Ra6, deemed a “highly dubious but excellent move” by commentators was sufficiently shocking to end the game with a full point for Deep Blue. Kasparov's suspicions and accusation of cheating no doubt affected his playing, and were likely factors in his missing a substantive chance for a draw in that Game 2 as pointed out in after-game analysis by his seconds, and his black thus had missed a chance for a critical half-point.

卡斯帕罗夫在第三局中固执地继续他的反计算机策略，即使白棋也是如此。一开始，他的1.d3可能从未在最高级别的国际象棋比赛中被用作开局。在等待深蓝像第一局那样犯错之后，卡斯帕罗夫让深蓝建立了坚不可摧的防御，如右图所示，卡斯帕罗夫提出平局，失去了白棋优势和半分，他的1.d3棋子在第三局结束时仍然孤零零地坐在那里。

Kasparov stubbornly continued his lay-back anti-computer strategy in Game 3, even with white. At the very outset, his 1.d3 was a move that likely had never before been used at the highest levels of chess as an opening. After presumably waiting for Deep Blue to blunder as it had in Game 1, Kasparov allowed Deep Blue to set up an impenetrable defense as shown in the figure at right, and Kasparov offered a draw, losing his white advantage and a half-point, his 1.d3 pawn forlornly still sitting there at the end of Game 3.

在第四局中，在修复了第一局中归因于评估软件错误的奇怪举动之后，在卡斯帕罗夫的第43^步棋时，“深蓝”由于一段监控并行搜索效率的代码而自行终止，如果效率降至给定水平以下，该代码就会终止程序，而事实确实如此，导致“深蓝”关闭，这让操作员许非常懊恼。

In Game 4, after the strange moves in Game 1 attributed to evaluation software bugs were repaired, upon Kasparov's 43^rd move, Deep Blue self-terminated owing to a piece of code that monitored the efficiency of a parallel search and terminated the program if the efficiency dropped below a given level, which it did, causing Deep Blue to shut down, much to the operator Hsu's chagrin.

深蓝必须重启，而根据人机对弈规则，重启时间由计算机承担。在时间压力下，深蓝的后续棋步并非最优，^第56步之后，深蓝残局 ROM显示出车残局和棋，卡斯帕罗夫也看到了，于是他随机出手黑棋。由于计算机编码异常，深蓝在白棋占优的情况下只得了半分。

Deep Blue had to be rebooted, and according to human vs. computer chess match protocol, the time it took to restart was charged to the computer side. Under time pressure, its subsequent moves were not optimal, and after the 56^th move, Deep Blue's endings ROM indicated a rook ending draw that Kasparov also saw, and playing black, he expediently offered. Because of the computer coding anomaly, Deep Blue thus only gained a half-point with the white advantage.

第五局，深蓝在棋子发展上占有明显优势，并下了颇具争议的11.h5，将黑线h兵从原位置往前推了两格（如右图所示），这一步让特级顾问们大吃一惊。然而，对许来说，这一步意味着深蓝在警告这位有史以来最伟大的棋手：“如果你在王翼易位，我就会攻击你！”这是一个大胆的威胁，没有一个人类棋手敢对卡斯帕罗夫发出这样的威胁。

In Game 5, Deep Blue had a significant advantage in piece development, and made the controversial 11.h5 move pushing the black h-file pawn forward two squares down from its original position as shown in the figure at right, a move that startled its Grandmaster advisors. However, the move meant to Hsu that Deep Blue was warning the greatest player who ever lived, “if you castle kingside, I will attack you!” It was an audacious threat that no human player would ever dare level at Kasparov.

事实上，卡斯帕罗夫赛后感叹，“没有电脑能下h5！”但许很清楚深蓝的硬件在做什么，⁷

Indeed, Kasparov post-match lamented, “no computer plays h5!” But Hsu knew exactly what Deep Blue's hardware was doing,⁷

当我看到深蓝的h5步时，我清楚地知道是什么硬件评估功能促成了这一步。在复赛前最后两个月的芯片设计中，我对硬件进行了重大修改，以评估王的安全度。在王易位之前，硬件会计算三组王的安全度评估，一组用于王翼易位，一组用于后翼易位，一组用于留在中心。真正的王安全度评估是三者的加权线性组合，权重基于三者的相对排名以及易位的难度。……在游戏位置上，深蓝总是可以安全地易位后翼，因此从它的角度来看，h5步是完全可以胜任的。

When I saw the move h5 from Deep Blue, I knew precisely what hardware evaluation features prompted the move. During the last two months of chip design before the rematch, I added drastic changes to the hardware for king safety evaluation. Before the king castles, the hardware computes three sets of king safety evaluations, one for kingside castling, one for queenside castling, and one for staying in the center. The real king safety evaluation is the weighted linear combination of the three, with the weighting based on the relative ranking of the three, and difficulty of making the castling moves. … In the game position, Deep Blue could always castle queenside safely, and therefore move h5 was perfectly capable from its point of view.

尽管卡斯帕罗夫后来已经准备好升级一个通路兵，但深蓝只是将其王向前推进并启动基于重复检查的平局序列，因此第五局比赛打成平局，卡斯帕罗夫的白棋再次只挽回了半分。

Although Kasparov later had a passed pawn ready to promote, Deep Blue just marched its king forward and initiated a drawing sequence based on repetition checks, so Game 5 was drawn, with Kasparov's white once again only salvaging a half-point.

五局过后，比分打成 2.5-2.5 平，而到了最后的第六局，除非执黑的卡斯帕罗夫能够击败拥有白棋优势的深蓝，否则计算机将追平或击败卫冕世界冠军，从而创造历史。

After five games, the score was tied 2½-2½ and for the final Game 6, unless Kasparov playing black could defeat a Deep Blue with white advantage, history would be made with a computer tying or beating a reigning world champion.

第六局之前，解说员们几乎都认为，一旦深蓝掌握了主动权，就无法阻挡了。事实上，深蓝如下图左所示，深蓝以11.Bf4开局，并且看到三个棋子的位置补偿，显然处于进攻模式。深蓝放弃了物质利益，以最终的王杀为目标，继续进攻，在19.c4时，卡斯帕罗夫认输。历史在下图右所示的最终棋局中被创造^。8

Before Game 6, the commentators now almost all believed that once Deep Blue had the initiative, it could not be stopped. Indeed, Deep Blue was out of its opening book with 11.Bf4 as shown in the figure below at left, and seeing three pawns worth of positional compensation, it was clearly in attack mode. Spurning material gains for an ultimate king kill, Deep Blue continued its attack and at 19.c4, Kasparov resigned. History was made with the final board shown in the figure below at right.⁸

尽管在第六局和比赛中都明显落败，但好斗的卡斯帕罗夫拒绝承认深蓝的优势，仍然认为 IBM 团队作弊了。他之前曾要求在比赛中查看深蓝的比赛日志，但 IBM 拒绝了，理由非常合理，因为这相当于在比赛过程中泄露比赛策略，就像人类在比赛中告诉对手他的策略和战术一样。IBM 同意在比赛结束后提供完整的比赛日志，以证明比赛中没有人工干预。

Despite a clear loss in Game 6 and the Match, a combative Kasparov refused to acknowledge Deep Blue's superiority, still believing that the IBM team had cheated. He had previously demanded to see Deep Blue's game logs during the Match, but IBM refused on the entirely reasonable grounds that that would be tantamount to revealing match strategy while the match was on-going, akin to a human telling his opponent his strategy and tactics during a match. IBM did agree to provide complete game logs after the Match to show that there was no in-game human intervention.

双方讨论了重赛，但卡斯帕罗夫要求他和他的团队提供更多奇怪的额外福利，并提议进行为期三周的比赛，中间休息两三天（显然是为了让卡斯帕罗夫恢复体力，而深蓝不需要休息）^。9

A rematch was discussed, but Kasparov's demands of further bizarre perquisites for himself and his team, and his proposed three-week match with two- and three-day rest periods (obviously for Kasparov to physically recoup, Deep Blue needed no rest periods).⁹

备受追捧的赞助商认为，这样的复赛形式太长，无法吸引公众的注意力，因此不愿提供赞助。IBM 为这场比赛提供了 70 万美元/30 万美元的胜者/败者奖金，支付了纽约最豪华的摩天大楼酒店的巨额费用，并为卡斯帕罗夫及其随行人员提供了一切便利设施，但已经实现了其目标，因此并不热衷。

Sought-after sponsors felt that such a rematch format was too long to hold public attention and were not forthcoming. IBM, having put up the $700,000/$300,000 winner/loser prize for the Match, paying for the considerable expenses of New York's poshest skyscrapers hotels, and accommodating Kasparov and his entourage every amenity, having already achieved its goal was not enthusiastic.

离开 IBM 后，为了消除人们对“深蓝”优越性的所有疑虑，许曾亲自安排与卡斯帕罗夫的重赛，但被卡斯帕罗夫的经理斥责为“缺乏信誉”并且没有足够的资金来支付奖金（至少一百万美元）。

After leaving IBM, in an effort to dispel all doubts of Deep Blue's superiority, Hsu personally tried to arrange a rematch but was denigrated by Kasparov's manager as “lacking credibility” and having insufficient funds for a prize (at least one million dollars).

深蓝战胜卡斯帕罗夫表明，自上而下的方法可以在受限领域内击败人类，尽管游戏之间需要对硬件和软件进行修复，而卡斯帕罗夫也知道这一点，因此选择了次优的移动策略。

Deep Blue's victory over Kasparov demonstrated that a top-down approach could defeat a human in a restricted domain, albeit with hardware and software fixes in-between games, and that Kasparov knew this and thus chose his sub-optimal move strategy.

这也许并不令人意外，但仍然令人焦虑，如果计算机是最好的棋手，人类比赛是否就会失去吸引力？国际象棋大师是否会被计算机科学家及其机器取代，相互对抗，争夺国际象棋霸主地位？

Unsurprisingly perhaps, but anxiety-inducing nevertheless, if computers are the best players, won’t human matches lose their appeal? Will Grandmasters be replaced by computer scientists and their machines playing against each other for chess supremacy?

至少公众对 2018 年世界象棋锦标赛上新晋世界冠军挪威棋手马格努斯·卡尔森与美国挑战者法比亚娜·卡鲁阿纳之间的比赛仍然有些兴趣。然而，这场比赛以 12 平局结束，最终以点球式快棋对抗（每位棋手总共 30 分钟）决定胜负，卡尔森获胜。

At least there was still some public interest in a match between the new world chess champion Norway's Magnus Carlsen and American challenger Fabiana Caruana in the 2018 World Chess Championship. It however ended in twelve draws, ultimately being decided by a penalty kick-like rapid chess confrontation (total 30 minutes per player) won by Carlsen.

如今，卡尔森和其他特级大师不再与计算机进行冠军赛，而是利用它们来磨练自己的技能。毫无疑问，人类世界象棋冠军的荣耀已被计算机所侵蚀，甚至更糟的是，由于计算机也接受了类似的训练，计算机可能还参与了许多高水平人类比赛中令人乏味的平局。

Carlsen and other GMs nowadays do not play championship matches against computers, but rather use them to hone their skills. The exaltation of a human World Chess Champion no doubt has been eroded by computers, and perhaps even worse, because of similar training on them, the computer may also have had a hand in the many stultifying draws of high-level human matches.

尽管“深蓝与卡斯帕罗夫”对决具有历史意义，但专家系统暴露出需要人工干预才能纠正的缺陷，而自上而下开发广泛专家系统的尝试也无法实现其预期目标。

Despite the historical significance of Deep Blue vs. Kasparov, the expert system revealed foibles that required human intervention to correct, and attempts to develop broad top-down expert systems would not fulfill their prospective destinies.

电视数学形式主义者认为，仅靠纯逻辑运算的公理就能产生定理，从而得出数学真理。直觉主义者祈求上天赋予某些人直觉，直觉与逻辑相结合，就能创造出揭示数学运算现实的方程式。自上而下的人工智能依靠人类构建的专家系统来实现指定目标。而自下而上的人工智能则依靠大数据的积累信息，经过算法逻辑的运算，就能找到基本事实。

The mathematical formalists believed that axioms operated upon by pure logic alone would produce theorems that lead to the mathematical truth. The intuitionalists invoked the Heavens to bestow certain humans with an intuition that together with logic would create the equations that revealed the mathematical operations reality. Top-down artificial intelligence relied on human-constructed expert systems operating to achieve a designated objective. Now bottom-up artificial intelligence relies on the accumulated information of Big Data, that upon undergoing algorithmic logic will find the ground truth.

所有这些方法都是“智能”的表现，而一位拥有令人敬畏的人类智能的人将建立通过算法将数据与基本事实联系起来的基本概念。

All of these approaches were manifestations of “intelligence”, and one man who was endowed with a fearsome human intelligence was to establish the fundamental concept that algorithmically linked the data to the ground truth.

数学神童诺伯特·维纳14岁大学数学专业毕业，随后又学习了动物学和哲学，能讲七种语言（据说所有这些语言都很难听懂），在哈佛大学发表了关于集合论的数理逻辑的论文，并在17岁时获得了博士学位。

The mathematics prodigy Norbert Weiner graduated from university in mathematics at age 14, further studied zoology and philosophy, could speak seven languages (and was said to be difficult to understand in all of them), wrote his Harvard dissertation on the mathematical logic of set theory, and received his Ph.D. at the tender age of 17.

他很快就成为数学精英中的一员，前往剑桥向传奇哲学家/数学家伯特兰·罗素和著名纯数学家 G. H. 哈代学习，后来又到欧洲数学和物理堡垒，在哥廷根与伟大的大卫·希尔伯特一起学习。

He was soon a member of the mathematics elite, traveling to Cambridge to learn from the legendary philosopher/mathematician Bertrand Russell and the renowned pure mathematician G.H. Hardy, and thence to the European citadel of mathematics and physics to study with the great David Hilbert at Gottingen.

凭借这份卓越的履历，多才多艺的维纳最初在哈佛大学教授哲学，但后来随着兴趣的不断变化，他先后在通用电气担任工程师以及在《波士顿先驱报》担任记者。

With this transcendent résumé, the eclectic Wiener first taught philosophy at Harvard, but then following continually diverging interests, took jobs as an engineer at General Electric and of all things a reporter for the Boston Herald.

1917 年，美国加入第一次世界大战，维纳渴望参军，但因视力不佳未能入伍，于是应数学家奥斯瓦尔德·凡勃伦的邀请，前往阿伯丁试验场研究炮弹弹道学，这是所有政府在战时都要求其最优秀的数学家做的事情。

With America's entry into World War I in 1917, eager to serve, but failing enlistment because of poor eyesight, Wiener was invited by the mathematician Oswald Veblen to the Aberdeen Proving Ground to work on artillery shell ballistics, something that all governments bade their best mathematicians to do in wartime.

第一次世界大战结束后，维纳未能获得哈佛大学的永久职位，他（和阿尔伯特·爱因斯坦）将此归咎于 GD Birkhoff 教授的反犹太主义观点，于是在麻省理工学院担任数学讲师^。1

After the Great War and being rejected for a permanent position at Harvard, for which he (and Albert Einstein) blamed on the anti-Semitic views of Professor G.D. Birkhoff, Wiener took a job as an instructor in mathematics at MIT.¹

在剑桥活跃的环境中，维纳定期与来自不同学科的知识分子会面，凭借自身多元化的背景，他开始对不同学科之间的边界研究感兴趣，这并不完全是跨学科研究，而是生物学、电子学、新型计算机以及最终关于身心问题的哲学思考之间的联系。

In the yeasty environment of Cambridge, Wiener joined regular meetings with intellectuals from many different disciplines, and with his own varied background, he became interested in the study of the boundary between different disciplines, not exactly interdisciplinary studies, but the nexus of biology, electronics, the new computers, and finally philosophical ruminations about the mind-body problem.

第二次世界大战期间，维纳重拾弹道学专业，研究如何用反应迟钝的高射炮打击高空快速移动的敌机这一棘手问题。目标总是在移动，对于战斗机来说，移动模式不一定是可预测的，不同的天气条件、不断变化的风向以及高射炮本身的倾向，所有这些都是一个非常复杂的问题，当时的手动机械射击指挥仪几乎无法应对^。2

During World War II, Wiener returned to his ballistics specialty to study the vexing problem of hitting high-flying and fast-moving enemy aircraft with slow-to-respond anti-aircraft guns. The targets were always moving, and for fighters, not necessarily in predictable patterns, and different weather conditions, changing winds, and the proclivities of the anti-aircraft guns themselves, all amounted to a very complicated problem with which the manual-mechanical firing directors of the day could hardly cope.²

在这里，维纳自己在动物学方面的研究以及与剑桥大学生物学家的多次讨论，使他想到了所有生物（包括人类）与其环境之间的联系，即自适应反馈回路，通过该回路，信息从人类在追求目标的过程中，会根据环境调整反应。正如查尔斯·达尔文在《物种起源》中所说：

Here Wiener's own studies in zoology and the many discussions with biologists at the universities in Cambridge, led him to the idea of the nexus between all creatures, including humans, to their environment, namely the adaptive feedback loop by which information is relayed from the environment to adjust responses in the pursuit of objectives. As Charles Darwin said in his Origin of the Species:

能够生存下来的并不是最强的物种，

也不是最聪明的，

但却是对变化最敏感的一个。

It is not the strongest of the species that survive,

nor the most intelligent,

but the one most responsive to change.

因此，任何智能机器都必须具备适应能力，因此他创造了控制论学科，即机器的“舵手”，体现了心身一元论^。3

It follows that any intelligent machine must be able to adapt, and so he created the discipline of cybernetics, the “steersman” of machines, exemplifying the monism of the mind-body.³

维纳和他的同事们随即设计了一种反馈控制系统，该系统可以根据雷达屏幕上目标飞机光点的移动来引导高射炮；遵循一个不断更新的反馈回路，然后通过启发式方法和一些快速计算，预测目标的轨迹并将其击落。

Wiener and colleagues thereupon devised a feedback control system that guided the anti-aircraft guns in response to the movement of the target aircraft's blip on a radar screen; a continually-updated feedback loop to follow and then through heuristics and some rapid calculations, predict the target's trajectory to shoot it down.

然而，巨大的成功并不是来自于对抗载人飞机，而是来自于第二次不列颠之战中对抗纳粹 V-2 火箭弹。据报道，在一次入侵中，新式火力指挥高射炮击落了 10 枚“飞行炸弹”中的 9 枚^。4

The great success, however, came not against human-piloted aircraft but rather against the Nazi V-2 rockets in the second Battle of Britain where reportedly in one incursion nine of ten of the “flying bombs” were shot down by the new fire director antiaircraft guns.⁴

沃伦·麦卡洛克是耶鲁大学医学院的神经生理学家，专攻癫痫和头部损伤。他的工作使他被任命为伊利诺伊大学精神病学研究实验室的负责人，这似乎与防空炮兵相去甚远。但在参加了一场关于维纳机器反馈理论的讲座后，他受到启发，意识到虽然大脑中的单个神经元在被激活时本身没有任何意义，而是对刺激作出反应，但神经元的集合及其突触连接形成的模式确实有意义，因此机器中的人工神经网络(ANN) 应该能够存储意义，从而获得知识，就像人脑一样。

Warren McCulloch was a neurophysiologist graduate from Yale Medical School with a specialty in epilepsy and head injuries. His work led to an appointment as head of the University of Illinois’ psychiatric research laboratory, seemingly a long reach from anti-aircraft gunnery. But after attending a lecture on Wiener's machine feedback theories, he was inspired to realize that although a single neuron in the brain when activated has no sense in and of itself, rather in response to a stimulus, an aggregate of neurons and their synaptic connections form a pattern that does have a sense, and therefore an artificial neural network (ANN) in a machine should be able to store sense, and thus gain knowledge, just like a human brain.

怀着这个想法，麦卡洛克向 18 岁的数学天才沃尔特·皮茨寻求帮助。皮茨指出，由于神经元的激活状态要么是开启，要么是关闭，因此可以对其进行二进制编码，突触模式可以遵循布尔代数来产生合乎逻辑且理想的结果。经过进一步的抨击，他推测克劳德·香农的双态开/关电子开关可以排列成产生一系列的逻辑模式，形成可以以电子方式模拟人类大脑推理能力的结果。

With this idea in mind, McCulloch sought the help of the 18-year-old mathematics prodigy Walter Pitts, who noted that since the neurons’ activation was either on or off, they could be binary coded, and the synaptic patterns could follow Boolean algebra to produce logical and desirable outcomes. Upon further fulmination, he surmised that Claude Shannon's two-state on/off electronic switches could be arrayed to produce cascades of logical patterns to form outcomes that could electronically model the human brain's ability to reason.

然后，对于人工神经网络来说，存储推理模式并通过反馈回路学习最佳的突触模式以达到该推理的期望结果只是一个合乎逻辑的步骤，从而赋予机器自适应智能，以有利地应对其在环境中遇到的不断变化的条件。

It was then just a logical step for the artificial neural network to store the reasoning patterns, and learn through a feedback loop the best synaptic patterns to reach the desired outcome of that reasoning, thereby endowing the machine with the adaptive intelligence to advantageously respond to the changing conditions it encountered in its environment.

在人工智能领域，这被称为自下而上的方法，即通过人工神经网络对人类大脑进行建模，该神经网络构建突触模式以响应外部刺激，通过数据集、启发式方法和实验进行监督训练，自下而上地学习。

In artificial intelligence circles, this came to be called the bottom-up approach of modeling the human brain by means of an artificial neural network that constructed synaptic patterns in response to external stimuli, learning bottom-up from supervised training from data sets, heuristics, and experimentation.

为了改进和加快学习速度，麦卡洛克的基本人工神经网络需要更复杂的反馈。20 世纪 50 年代末，在维纳跨学科联系的另一个例子中，康奈尔精神病理学家弗兰克·罗森布拉特 (Frank Rosenblatt) 通过在人工神经元激活水平上附加权重来增加人工神经网络响应的细微差别，通过“调节”反馈来更好地向 ANN 呈现观察结果和数据，从而促进更快地学习反馈信息中的重要内容，从而使双态人工神经元更容易受到影响。罗森布拉特将他的加权人工神经元称为感知器。

In order to improve and hasten learning, McCulloch's basic artificial neural network needed more sophisticated feedback. In the late 1950s in another example of Wiener's interdisciplinary nexus, Cornell psychopathologist Frank Rosenblatt made the two-state artificial neuron more impressionable by attaching a weight to the artificial neuron activation level to add nuance to the artificial neural network's response, by “modulating” the feedback to better present observations and data to the ANN, thus promoting more rapid learning of what is significant in the feedback information. Rosenblatt called his weighted artificial neuron a perceptron.

感知器最早用于计算机视觉。一组光电管聚焦于两个正方形的测试图像的特定区域。通过光电效应，图像反射的光子被转换成模拟电信号，这些信号被数字化，以灰度映射到存储在 IBM 704 计算机内存中的像素矩阵上。

The perceptron was first used in computer vision. A bank of photoelectric cells focused on particular regions of a test image of two squares. The reflected light photons from the image were converted into analog electrical signals through the photoelectric effect, and those signals were digitized for greyscale-mapping onto a pixel matrix stored in the memory of an IBM 704 computer.

通过以电子方式加权每个像素的激活水平来反映测试图案的明暗图案的强度，迭代和累积重复将在计算机感知器网络上准确再现目标方块，从而产生人工神经网络模式识别的第一个实例。

By electronically weighting each pixel's activation level to reflect the intensities of the light and dark patterns of the test pattern, iterative and cumulative repetition would produce an accurate rendition of the target squares on the computer's network of perceptrons, thereby producing the first instance of artificial neural network pattern recognition.

重要的是要认识到，IBM 704 不仅仅是像电视摄像机一样将图像重现到视频屏幕上显示，它的人工神经网络还识别了两个正方形的特征并将其存储在内存中，并且原则上一旦这样做了，感知器网络就学会了通过将新查看图像的像素模式与内存中存储的正方形模式进行比较来识别该类型的模式为正方形，这可能对将来识别由正方形构造组成的物体很有用。

It is important to realize that the IBM 704 has not just reproduced the image to display on a video screen like a TV camera, its artificial neural network has recognized the features of two squares for storage in memory, and in principle once having done so, the perceptron network has learned to identify patterns of that type to be squares by comparing the pixel patterns of a new viewed image with the stored squares pattern in memory, useful presumably for future identification of objects comprising square conformations.

然而，麻省理工学院的马文·明斯基 (Marvin Minsky)在其 1969 年出版的《感知器》一书中指出，感知器的组合二进制电路无法执行 XOR 逻辑功能，因此在理论上应用会受到限制。明斯基的论点后来被分层感知器网络推翻，但在此之前，它使人工智能神经网络研究陷入了长达十年的人工智能寒冬，直到 1981 年日本第五代计算机项目失败后才得以解冻，该项目在又一个十年后失败，引发了 20 世纪 90 年代初的另一个人工智能寒冬^。5

In his 1969 book Perceptrons, MIT's Marvin Minsky however, argued that the perceptrons’ combinatory binary circuits could not perform the XOR logical function, and would thus be theoretically limited in application. Minsky's thesis was later disproved by a layered network of perceptrons, but not before it chilled AI neural network research into a ten-year AI Winter that thawed only to encounter the ill-fated Japanese Fifth Generation project begun in 1981, which failure after another ten years triggered yet another AI Winter of the early 1990s.⁵

在明斯基错误的“冬天”理论之后，加州理工学院于 1982 年重新建立了人工神经网络，将记忆建模为突触模式中人工神经元的可变能级，这为感知器在人工智能中的应用提供了强有力的概念验证动力。

After Minsky's false Winter, the California Institute of Technology in 1982 rehabilitated the artificial neural network, modeling memory as variable energy levels of artificial neurons in a synaptic pattern, a strong proof-of-concept impetus for the use of perceptrons in artificial intelligence.

电视思考机器的功能操作模型可以用一个简单的映射函数来表示，

The functional operations model for a thinking machine can be represented by a simple mapping function,

给定输入变量x（刺激），模型f(x)将它们映射到输出y（响应），如下图所示。

where given the input variables x, the stimulus, the model f(x) maps them onto the output y, the response as schematically shown in the figure below.

在监督学习中，如果输出y与标记的输入数据不准确匹配，则输出与标记的训练数据之间的差异（误差）将被最小化，并将调整后的新数据反馈到算法中，如图所示。如果经过多次迭代误差最小化后，算法仍然没有产生准确的结果，那么算法本身可能需要系统校准。

In supervised learning, if the output y does not accurately match the labeled input data, the difference between the output and the labeled training data (the error) will be minimized and the adjusted new data fed back into the algorithm as shown in the figure. If after many iterated runs of error minimization, the algorithm still does not produce accurate results, then the algorithm itself may require a system calibration.

经过监督训练，模型大概已经学习到了训练集数据的共同特征，并且能够概括这些特征来识别新图像、概率分布，或对呈现给模型的新的非结构化和未标记数据进行分类。

After supervised training, the Model presumably has learned the common characteristics of the training set data, and is able to generalize those characteristics to recognize new images, probability distributions, or perform classification on new unstructured and unlabeled data presented to the Model.

在人工神经网络中，映射函数f(x)是通过在一组标记数据上训练网络而构建的；也就是说，通过抽象标记训练集数据中发现的共同特征进行归纳，形成一个模型概括，通过演绎来识别新出现的数据，从模型到具体情况。

In artificial neural networks, the mapping function f(x) is constructed by training the network on a set of labeled data; that is, by induction from the abstracting of common characteristics found in the labeled training set data to form a model generalization for recognizing newly-presented data by deduction, going from the model to a particular case.

泛化的数学定义是，¹

A mathematical definition of generalization is,¹

存在一组元素，这些元素具有共同的特征，足以形成一个可以执行演绎推理的概念模型

There exists a set of elements that possesses common characteristics shared by those elements sufficient to form a conceptual model that can perform deductive inferences

换句话说，训练集数据必须具有足够的共同特征来配置模型，以便其推导出的概括可以将新数据归类为属于某个集合，或者预测任何新数据所暗示的后果。

In other words, the training set data must have sufficient common characteristics to configure the model so its deduced generalizations can classify new data as belonging to some set, or predict the consequences that any new data implies.

模型f(x)分类和预测的效果取决于模型对新数据的拟合优度。当模型无法从训练数据集中归纳出任何内容时，它属于欠拟合；或者属于过拟合，这意味着它与训练集过于接近，只能识别与训练集数据几乎完全相同的新数据。就像金发姑娘会选择不太热或不太冷的粥一样，当模型应用于新数据时，它恰到好处地拟合；也就是说，它识别了它应该识别的内容。

How well the model f(x) can classify and predict is determined by the goodness of fit of the model on the new data. The model underfits when it cannot generalize anything from the training dataset, or it can overfit, meaning that it is too closely allied with the training set and can only recognize new data that is almost exactly the same as the training set data. Like Goldilocks who chooses the porridge that is not too hot or cold, when the model is applied to new data, it fits just right; that is, it recognizes what it should recognize.

当模型不能充分捕捉训练数据的抽象共同特征时，我们就称其为欠拟合。从统计分析的角度来看，欠拟合模型的方差低、偏差高。这意味着它们在吸收训练集数据时不会发生太大变化（方差低）并且模型对数据的假设太强（偏向自身）。

A model is said to underfit when it cannot adequately capture the abstract common characteristics of the training data. In statistical analysis terms, underfitting models have low variance and high bias, meaning that they do not change much in absorbing the training set data (low variance) and the model's assumption about the data is too strong (biased towards itself).

例如，如果用直线建模一组分布非常广泛的数据点，那么无论分布如何变化，该模型都会持续存在，并且它做出了过于强烈的假设，即数据可以通过一条简单的直线来概括，而多项式曲线可能更好地拟合数据。

For example, if a very widely distributed set of data points is modeled by a straight line, the model persists no matter how varied the distribution is, and it makes a too strong assumption that the data can be generalized by a simple straight line, whereas for instance a polynomial curve might better fit the data.

欠拟合很容易从模型在训练集数据上的表现不佳中发现；其分类或预测与训练数据上的标签不匹配。欠拟合通常是由于模型训练不足造成的，补救措施是提供更多的训练集数据和更多的数据周期（运行）。然后可能会出现所需的泛化，因为更多的训练使模型更加敏感，从而能够更准确地识别数据所代表的内容。

Underfitting is easy to detect from the model's poor performance on the training set data; its classifications or predictions do not match the labels on the training data. Underfitting is commonly caused by under-training the model, and the remedy is simply to provide more training set data and more epochs (runs) through that data. The desired generalizations may then emerge because more training has rendered the model more sensitive, and thus able to more accurately recognize data for what it represents.

过度拟合在统计上与欠拟合相反，它具有高方差和低偏差，这意味着过度拟合将不相关的数据或噪声纳入模型（高方差），因此在呈现新数据时过于紧密地遵循训练集数据，使得模型的假设很弱（对自身的低偏差），结果过度拟合的模型将无法识别实际上在模型期望泛化范围内的新数据。

Overfitting is the statistically opposite of underfitting in that it has high variance and low bias, meaning that overfitting has included irrelevant data or noise into the model (high variance) and thus too closely follows the training set data when presented with new data, so that the model's assumptions are weak (low bias towards itself), with the result that the over-fitted model will not recognize new data that is actually within the purview of the model's desired generalization.

牛津词典对过度拟合的定义是， ²

A definition of overfitting from the Oxford Dictionary is,²

分析结果与某组特定数据过于接近，因此可能无法拟合新数据或可靠地预测未来的观测结果。

The production of an analysis that corresponds too closely to a particular set of data, and may therefore fail to fit new data or predict future observations reliably.

同样，机器学习模型过度拟合是指模型在不经意间将训练集数据中不相关的细节或噪音纳入其泛化中，好像它们是训练数据的基本抽象共同特征的一部分。过度拟合意味着模型训练过度，就像一个勤奋但愚钝的小学生，他只是死记课本上的数学问题解决方案，而不是从问题中学习抽象的概括，以便将其应用于考试中的新问题。

Again, the machine learning model overfits when the model unwittingly incorporates irrelevant detail or noise in the training set data into its generalization as if those were part of the essential abstracted common characteristics of the training data. Overfitting means that the model has been over-trained, and like the diligent but dull schoolboy who has simply memorized the math problem solutions in the textbook instead of learning the abstract generalizations from the problems such that he can apply them to new problems on an examination.

自下而上的人工智能中过度拟合的一个例子是过于详细的决策树，它包含太多与广义抽象无关的分支和叶子，并包含偶然的噪声，以至于在混乱的无关信息中，很难识别新数据所代表的内容。

An example of overfitting in bottom-up artificial intelligence is an overly detailed decision tree that includes too many branches and leaves irrelevant to generalized abstraction and contains incidental noise, so much so that in the jumble of extraneous information, it is difficult to recognize new data for what it represents.

补救措施当然是谨慎地修剪决策树，例如通过 alpha-beta 丢弃不高效的分支。谨慎的做法是通过重采样来实现的，例如k 倍交叉验证，这只是一种花哨的说法，即取不同的训练数据子集，对子集进行k次训练和测试，并根据子集测试结果观察模型性能，然后对整个模型进行适当的调整。

The remedy of course is to prudently prune the decision tree, for example by alpha-beta discarding unproductive branches. Prudence is exercised by resampling, for instance k-fold cross validation, which is just a fancy way of saying take different subsets of the training data, train and test the subsets k times, and observe the model performance in regard to the subset test results, and then make appropriate adjustments to the overall model.

另一种解决过度拟合的方法是分离出训练数据的一个较大的子集，用作验证数据集，以测试在其余数据上训练的不同模型，这些模型是从每个模型中的误差函数最小化发展而来的。然后通过验证数据集测试每个模型的性能，以查看哪个模型相对于标记数据集的误差最小。验证数据集已成为提高机器学习算法准确性的重要工具。

Another overfitting cure is to separate a larger subset of the training data to use as a validation dataset to test different models trained on the rest of the data and developed from the minimization of the error function in each model. The performance of each model is then tested by the validation dataset to see which model has the smallest error in respect of the labeled dataset. The validation dataset has become an essential tool for promoting machine learning algorithm accuracy.

当模型在训练数据和验证数据集上的表现随着时间的推移而提高时，该模型就是拟合度较高的。但是，需要注意的是，仅仅进行更多的训练实际上会通过过度训练而降低模型的性能，因为过度训练会导致模型与训练集数据过度拟合。此外，进行太多次验证数据集运行可能会导致模型学习验证集数据和训练集数据，就像聪明的女学生从测验中了解到期末考试的内容一样。

The model good-fits when its performance over time on the training data and validation datasets improves. However, it is important to note that simply doing more training can actually decrease the model's performance through overtraining that overfits the training set data. Furthermore, doing too many validation dataset runs may well cause the model to learn the validation as well as the training set data, like the clever schoolgirl who gleans from the quizzes what will be on the final examination.

在这种情况下，可以运行一个独立于训练数据集但遵循与训练数据集相同概率分布的测试数据集。如果结果与运行的训练数据集相似，则表明模型没有过度拟合。这就是聪明的女学生的情况，她学会了如何概括一门课程的所有主题，从而理解了这门课程的精髓。

In this case, a test dataset that is independent of the training dataset but follows the same probability distribution as the training data set can be run. If the results are similar to the training data set run, that is an indication that the model does not overfit. This is the case of the brilliant schoolgirl who has learned how to generalize all the subject matter of a course, thereby understanding the essence of the subject.

通过观察模型在训练过程中准确识别标记训练集数据的改进率，可以找到最佳训练方案，当改进率接近零时，应停止训练以避免过度拟合。这就像一位能干的学校老师，他敏锐地介绍更高级的主题，以避免学生对常规内容感到无聊。

Finding the optimum training regime can be achieved by observing the rate of improvement of the model in accurately recognizing the labeled training set data over the training epochs, and when the rate of improvement approaches zero, the training should be stopped to avoid overfitting. This is like the able schoolteacher who perceptively introduces more advanced topics to avoid boring the students with routine material.

欠拟合和过拟合是困扰人工神经网络的双重困扰；幸运的是，除了验证和测试数据集之外，机器学习建模中还有许多方法可以处理它们。

Underfitting and overfitting are the twin gremlins plaguing artificial neural networks; fortunately in addition to validation and test datasets, there are many ways of dealing with them in machine learning modeling.

可以采用不同的权重和偏差参数初始化，例如贝叶斯、高斯混合模型和因子分析来调整人工神经网络以驱逐小精灵^。3

Different weights and biases parameter initializations can be employed, such as Bayesian, Gaussian Mixed Model, and Factor Analysis to tune the artificial neural network to expel the gremlins.³

模型欠拟合和过拟合也可以通过正则化方法（例如超参数L1和L2、dropout和训练数据的人工扩展）来缓解。

Model underfitting and particularly overfitting both also can be alleviated by regularization methods such as the hyperparameters L1 and L2, dropout, and artificial expansion of the training data.

隐藏层中的神经元太少可能会导致从数据中提取的特征图丢失重要特征，从而严重欠拟合输入数据。另一方面，在隐藏层中使用过多的神经元可能会导致激活无关数据和噪声，从而严重过拟合数据。在这种情况下，网络的处理能力太强，以至于训练集中的数据太有限，无法训练隐藏层中的所有神经元，神经元会“找到”并错误地解释无关数据。

Too few neurons in the hidden layers may result in feature maps extracted from the data that miss significant characteristics, seriously underfitting the input data. While on the other hand, using too many neurons in the hidden layers can result in activating irrelevant data and noise, seriously overfitting the data. In this case, the network has so much processing capacity that the data in the training set is too limited to train all the neurons in the hidden layers, and the neurons “find” and falsely interpret extraneous data.

可以通过将层中随机选择的一组激活值全部设置为零来缓解训练集数据因过多神经元而过度拟合的问题。因此，这是对网络清晰度的测试，因为模型应该能够选择正确的泛化，而不管某些激活值是否缺失^。4

The overfitting of training set data by excess neurons can be alleviated, simply by dropping out a randomly-chosen set of activations in a layer by setting them all to zero. This is therefore a test of network perspicuity in that the model should be able to choose the right generalizations regardless of the absence of some activations.⁴

在dropout中，会丢弃不同的神经元组，因此就像在每次 dropout 事件后训练不同的神经网络一样，这些不同的网络会以不同的方式过度拟合数据，因此取它们的平均结果会奇怪地缓解过度拟合。正如现代人工智能的先驱之一、2018 年图灵奖获得者 Yann LeCun 所解释的那样，

In dropout, different sets of neurons are dropped, so it is like training a different neural network after each dropout event, and these different networks will tend to overfit the data in different ways, so taking their average results will curiously alleviate the overfitting. As one of the pioneers of modern AI and a recipient of the 2018 Turing Award Yann LeCun explained,

这种技术减少了神经元的复杂协同适应，因为神经元不能依赖于其他特定神经元的存在。因此，它被迫学习更强大的特征，这些特征与其他神经元的许多不同随机子集结合使用时很有用。

This technique reduces complex co-adaptations of neurons, since a neuron cannot rely on the presence of particular other neurons. It is, therefore, forced to learn more robust features that are useful in conjunction with many different random subsets of the other neurons.

亨利·基辛格曾评价德国总理古斯塔夫·施特雷泽曼对第一次世界大战后非常敏感的德国裁军问题的精明处理：“随着时间的推移，他的战术变成了战略，权宜之计变成了信念。” ⁵

To paraphrase Henry Kissinger on Chancellor Gustav Stresemann's astute handling of the very sensitive issue of German disarmament after World War I, “Over time [his] tactics become strategy and the expedient, conviction”.⁵

另一方面，人为地扩展训练数据可以使人工神经网络模型更加真实，例如在改进语音识别方面，添加背景噪音以最适合真实的聆听情况。

On the other hand, artificially expanding the training data can make the artificial neural network model more realistic, for example in improved speech recognition, adding background noise to best-fit real-life listening situations.

过度拟合也可以通过正则化技术来改善，例如权重衰减（L1 正则化），它为成本函数添加了一个项，从而稳定了其梯度下降，当人工神经网络的不同运行导致完全不同的结果时，这种方法非常有用。在L2 正则化中，通过添加权重绝对值的总和来修改成本函数，以稳定其梯度下降反向传播^。6

Overfitting can also be ameliorated by regularization techniques, such as weight decay (L1 regularization), which adds a term to the cost function, thereby stabilizing its gradient descent, proving useful when different runs of the artificial neural network result in quite different results. In L2 regularization, the cost function is modified by adding the sum of the absolute values of the weights for stabilization of its gradient descent backpropagation.⁶

米宏观自然现象和工程系统的数学模型几乎总是采用二阶偏微分方程的形式。对于确定性物理系统，这些方程大多是线性的，这意味着导数项的系数是常数或仅是独立变量（而不是因变量）的函数，并且不存在相互相乘或自身平方、立方或更高次方的导数。

Mathematical models of macroscopic natural phenomena and engineering systems almost always take the form of second-order partial differential equations. For deterministic physical systems, those equations are mostly linear, meaning that the coefficients of the derivative terms were constants or functions only of an independent variable (and not a dependent variable), and there were no derivatives multiplying each other or themselves squared, cubed or raised to higher powers.

对于相对简单的系统，线性微分方程通常可以以封闭形式求解，即以多项式、正弦、余弦、指数、自然对数及其组合的基本函数形式求解，这些解将充分描述不同初始和边界条件下的物理情况，从而允许进行数学建模和预测^。1

For relatively simple systems, linear differential equations often could be solved in closed form, meaning in terms of the elementary functions of polynomials, sine, cosine, exponentials, natural logs, and combinations thereof, and these solutions would fully describe the physical situation under different initial and boundary conditions, thereby allowing mathematical modeling and prediction.¹

然而，现实生活中的大多数物理系统几乎总是非线性的，因此无法以封闭形式求解，因此首先使用早期微分分析仪的齿轮的微小机械转动的有限差分，然后以数字方式增加独立变量并相应地区分因变量，方程式最初是通过年轻女性使用加法机手工求解的，求解速度非常慢；后来，通过数字计算机编程，并采用导数来加速收敛，求解速度非常快^。2

However, most physical systems in real life are almost always non-linear, and thereby not solvable in closed form, so using the finite-differences first of tiny mechanical turns of cogwheels of the early differential analyzers, and later digitally incrementing the independent variable and correspondingly differentiating the dependent variable, the equations were solved numerically at first very slowly by hand using young women and adding machines, and later very quickly by programming using digital computers, and taking derivatives to hasten convergence.²

除了困难之外，现实世界的情况非常复杂，涉及微分方程中多个分量和项所表示的许多因素、许多不同的独立变量和因变量以及各种相关参数，每种情况都需要不同的初始条件和边界条件。

Adding to the difficulties, the complexities of real world situations involved many factors represented by multiple components and terms in the differential equations, many different independent and dependent variables, and all manner of associated parameters, each situation requiring different initial and boundary conditions.

此外，牛顿力学在分子、原子和原子核的世界中并不成立，在这些世界中，薛定谔的量子力学二阶微分方程和海森堡的矩阵处理的是微观波函数形成和坍缩的玻恩概率，而不是牛顿宏观计算的决定论。

Newtonian mechanics furthermore did not hold in the world of molecules, atoms, and nuclei, where the quantum mechanical second-order differential equations of Schödinger and the matrices of Heisenberg dealt with the Born probabilities of microscopic wavefunction formation and collapse, rather than the determinism of a Newtonian macroscopic calculation.

蒙特卡罗和原子弹

Monte Carlo and the Atomic Bomb

然而，对于多体系统，统计平均值可以从宏观特征的角度表示系统的整体行为；例如，由数十亿个微观原子组成的气体的热力学描述的压力、体积和温度的统计力学推导。

For many-body systems, however, a statistical average could represent the overall behavior of the system in terms of macroscopic characteristics; for example, the statistical mechanics-derived pressure, volume, and temperature of a thermodynamical description of gases composed of billions of microscopic atoms.

原子弹之所以会释放能量，是因为在高裂变率的放射性铀235（²³⁵ U）或钚（²³⁹ Pu 和²⁴¹ Pu）的原子核分裂过程中，裂变碎片的质量小于原原子核的质量。根据爱因斯坦著名的质能等价方程E = mc ² ，这种质量亏损相当于原原子核中质子和中子的结合能的释放^。3

The Atomic Bomb releases energy because in the splitting of the nucleus of the high fissile rate of radioactive uranium-235 (²³⁵U) or plutonium（²³⁹Pu and ²⁴¹Pu）the masses of the fission fragments are less than the mass of the original nucleus. That mass defect, according to Einstein's famous mass-energy equivalence equation E = mc², is equivalent to a release of the binding energy of the protons and neutrons in the original nuclei.³

原子弹爆炸时，原子核分裂，释放出²³⁵ U 的质子和中子，虽然带正电的质子会避免与其他质子碰撞，但中性中子会与其他²³⁵ U 或²³⁹ Pu 原子核碰撞，引发进一步的核裂变并再次释放出大量的质子和中子。当核裂变有效中子增殖系数k = 1时，^235U或^239Pu的数量已达到临界质量，从而引发自发的链式裂变反应，在核爆炸中突然释放出所有的质子和中子的结合能。

The Atomic Bomb explodes when a nucleus is split, protons and neutrons of ²³⁵U and are released, and although the positively-charged protons tend to avoid collisions with other protons, the neutral neutrons will collide with other ²³⁵U or ²³⁹Pu nuclei instigating further nuclear fission and again releasing copious protons and neutrons. When the nuclear fission effective neutron multiplication factor k = 1, the amount of ²³⁵U or ²³⁹Pu has reached a critical mass resulting in a spontaneous chain reaction of fission reactions, suddenly releasing all the proton and neutron binding energies in a nuclear explosion.

在设计原子弹时，科学家首先尝试使用二阶微分和积分方程来确定中子与铀核碰撞以及随后释放更多中子的过程。然而，在扩散级联碰撞中，每次碰撞都会产生超过十亿个中子，每个中子可能会继续与数十亿个其他铀核碰撞，而碰撞会在后续碰撞树的不断扩散的分支中产生数十亿个中子，这显然不适合对每个中子进行确定性运动学（运动研究）计算。

In designing the A-Bomb, scientists first tried to use second-order differential and integral equations to deterministically follow the neutrons in their collisions with the uranium nuclei and the subsequent release of more neutrons. However, in the spreading cascade of collisions where each collision could produce more than a billion more neutrons, and each neutron could go on to collide with billions of other uranium nuclei, and the collisions would produce even more billions of neutrons in ever-spreading branches of a tree of subsequent collisions, it was clearly not amenable to a deterministic kinematic (study of motion) calculation of each and every neutron.

而且，每次碰撞、裂变和释放中子事件都是量子力学的，无法绝对确定，只知道碰撞事件的概率，而且所有过程还受反应室内的初始条件和炸弹外壳的边界条件的影响。

Furthermore, each collision, fission, and release of neutrons event was quantum mechanical and thus could not be absolutely determined, only the probabilities of collision events were known, and all of the processes were further subject to the initial conditions in the reaction chamber and the boundary conditions of the Bomb casing.

参与原子弹研制的人之一是数学家斯坦尼斯拉夫·乌拉姆，他是来自1935年受到德国威胁的波兰的移民，他于1943年加入洛斯阿拉莫斯团队，从事中子通量问题分析的工作，但在运动学研究方面的成功并不比其他人多。

One of those participating in the development of the Atomic Bomb was the mathematician Stanislaw Ulam, an immigrant from a Poland threatened by Germany in 1935, he joined the Los Alamos team in 1943, taking up work on analyzing the neutron flux problem, but with no more success in the kinematics study than others.

当然，曼哈顿计划最终根据中子气体通量的温度、压力、密度要求以及弹腔体积，并通过实验进行了实际设计，并给出了完善的设计。

Of course, the Manhattan Project ultimately produced a sound design based on the temperature, pressure, and density requirements of the neutron gas flux and the volume of the bomb cavity, and practically engineered through experimentation.

然而，铀临界质量中子通量问题一直困扰着乌拉姆，1945 年，当他患上病毒性脑炎时，他被关在医院里，无事可做，只能整天玩纸牌，而且他一直这样做，直到现在。

The uranium critical mass neutron flux problem stuck with Ulam, however, and in 1945 when struck with viral encephalitis, he was confined to hospital with nothing to do but play solitaire all day, which he did, over and over again.

乌拉姆像数学家一样思考，他想知道是否有办法找到成功完成每场游戏的关键，因此他开始记录纸牌的顺序、玩法和游戏的最终布局，并开始相信，如果他能观察足够多的游戏，他可能能够从统计上发现一些导致成功的游戏模式，然后将纸牌布局建模为描述气体整体的热力学压力、温度和体积的统计力学，从而描述单人游戏的整体行为。

Thinking like the mathematician that he was, Ulam wondered if there was any way he could find keys to successfully complete each game, so he began to record the sequence of cards and their play and the game's final layout, and came to believe that if he could just observe a large enough number of games, he might be able to statistically discover some patterns of play that led to success and then model the card layouts analogous to the statistical mechanics of thermodynamic pressure, temperature, and volume describing a gas as a whole, and thus describe the overall behavior of solitaire games.

因为一副 52 张牌的扑克牌的排列方式比我们银河系中的原子数量（约 10 ⁶⁷）还要多，而且每次良好的洗牌都会产生完全不可预测的初始排列顺序，所以从扑克牌中抽出的牌的顺序总是随机的。尽管抽出的牌只有几种放置可能性，但是每种玩法对成功结论的贡献都有不同的战略概率。此外，牌的放置选择取决于牌之前的布局状态，而牌的放置会改变布局状态。所有这些概率和牌的布局对于每场游戏来说都是不同的，因此需要进行天文数字般的游戏才能发现任何宏观的成功关键（如果确实存在的话）。

Because the cards in a 52-card deck can be arranged in more ways than the number of atoms in the our galaxy (about 10⁶⁷), and a good shuffle results in a completely unpredictable initial arrangement every time, the sequence of cards drawn from the deck will always be random. And although there were only a few placement possibilities for a drawn card, there were different strategic probabilities for each play as to its contribution to a successful conclusion. Furthermore, the card placement choices would depend on the preceding layout state of the cards, and a card placement would change the layout state. All of these probabilities and card layouts would be different for each game, so an astronomical number of games would be required to discover any macroscopic keys to success, if such indeed existed.

乌拉姆意识到所有这些条件都必须包含在任何游戏模型中。他开始思考，他知道马尔可夫链是随机变量序列X _i (卡片) 的随机集合，这些变量属于有限配置空间 (卡片布局)，这些空间由通过链 (卡片放置可能性) 连接的分离节点组成，代理可以选择在其中行走，但分配了到其他节点 (卡片放置可能性) 的步数概率P _ij，其中过程中状态的概率分布仅取决于当前状态 (卡片布局)，而不取决于任何过去的状态 (马尔可夫性质)。

Ulam realized all of these conditions would have to be included in any model of the game. He began to think, he knew that a Markov chain is a stochastic ensemble of a sequence of random variables X_i (cards) belonging to a finite configuration space (card layout) of separated nodes connected by chains (card placement possibilities) among which an agent can choose to walk but with assigned probabilities P_ij of steps to other nodes (card placement possibilities), whereby the probability distribution of states in the process depends only on the present state (card layout) and not on any past states (the Markovian property).

下图显示了马尔可夫链的示意图，其中概率转移矩阵P ，其中P矩阵的每个元素表示从 A 到 B 和 C、从 B 到 A 和 C、从 C 到 B 和 A 以及在每种情况下都回到自身的概率。

A schematic example of a Markov chain is shown in the figure below with the transition matrix of probabilities P, where each element of the P matrix represents the probability of a step from A to B and C, B to A and C, C to B and A, and steps in every case to itself.

从数学上来说，过渡矩阵P的各个元素由下式给出：

Mathematically, the individual elements of the transition matrix P are given by

${磷}_{我杰}=磷rob\mathrm{一个}b我升我吨是（{十}_{钾+1}=杰\mid {十}_{钾}=我）。$

$P_{ij}=Probability(X_{k+1}=j\mid X_k=i).$

如果代理可以移动到链中的任何其他节点的概率为正，无论概率多低，则该概率是不可约的；如果代理不能在相同节点的循环中无休止地循环，则该链是^非周期性的；如果代理可以探索每个节点，则该链是遍历性的。4

If there is a positive probability, no matter how low, that an agent can move onto any other nodes in the chain, it is irreducible; if the agent cannot go around endlessly in cycles of the same nodes, the chain is aperiodic; and if the agent can explore every node, the chain is erdogic.⁴

马尔可夫链是单人纸牌游戏的完美模型，因为它完全满足了游戏的要求。洗牌后的一副牌是随机分布的，但在玩单人纸牌游戏时，手中牌的可能摆放范围是有限的，这有利于达到最终目标。乌拉姆发现，在可能的输入（打牌）范围内，每种玩法都有确定的概率，与其达到所有牌都排列在最终阵列中的目标的有效性相称，经过确定性计算后，根据单人纸牌游戏规则，给定特定输入会产生相同的输出，他可以使用马尔可夫链来模拟游戏。

The Markov chain was a perfect model for solitaire as it completely satisfied the game's requirements. A deck of cards after shuffling is randomly distributed, but in playing solitaire, there are restricted domains of possible placements of the card in hand that will go towards reaching the final objective. Ulam found that within the domain of possible inputs (the playing of a card), there would be a definite probability for each play commensurate to its efficacy in reaching the objective of all the cards being in the final array, and after a deterministic computation whereby the same output is produced given a particular input according to the rules of solitaire, he could model the game using a Markov chain.

至于不可预测性，洗好的牌堆中牌的随机分布可以通过对代表牌的数字进行随机分布采样来获得，然后通过反复采样和汇总结果，如果他可以模拟足够数量的游戏，他就能发现成功的关键，例如存在的。

As for unpredictability, the random distribution of cards in a shuffled deck could be taken from sampling a random distribution of numbers representing the cards, and then by repeated sampling and aggregating the results, if he could simulate a sufficient number of games, he could discover the keys to success, such that existed.

采用随机分布的模拟被称为“蒙特卡罗”，以拉斯维加斯一家赌场的名字命名，而拉斯维加斯本身又以欧洲赌博之都的名字命名，这体现了赌博业宣传的完全随机的获胜机会，其中不包括赌场的保证利润，因为这是建立在大数定律的基础上的。它也被称为伯努利定律，它是任何活动在经过大量试验后最终回归均值的结果（赌博中的均值总是在庄家这边），也是蒙特卡罗模拟复杂系统有效性的基础⁵。

A simulation employing a random distribution is called “Monte Carlo” after the name of a casino in Las Vegas itself named after the gambling capital of Europe, evincing the gambling industries’ propaganda of a completely random chance at winning, something that does not include the assured profits of the casino, based as that is on the Law of Large Numbers. Also called Bernoulli's law, it is the ultimate regression to the mean of any activity after a very large number of trials (the mean in gambling is always with the house), and is the foundation of the efficacy of a Monte Carlo simulation of a complex system⁵.

当统计样本N的大小趋近于无穷大时，方差 σ ²（即标准差的平方平均值σ是衡量数据与算术平均值μ之间变异性的指标）将趋近于零，回归到均值概率将趋近于任何活动的真实概率。标准差σ衡量数据的离散程度，它只是方差的均方根，

As the size of a statistical sample N approaches infinity, the variance σ², which as the average squared standard deviations σ is a measure of the variability of data from the arithmetic mean μ, will approach zero, and the regression to the mean probability will approach the true probability of any activity. The standard deviation σ measures the dispersion of the data, and is just the root mean square of the variance,

${\sigma }^2=\frac{1}{否}\sum _{我}{（{十}_{我}-\mu ）}^2\mathrm{和}\sigma =\sqrt{\frac{1}{否}\sum _{我}{（{十}_{我}-\mu ）}^2}$

${\sigma }^2=\frac{1}{N}\sum _i{(x_i-\mu )}^2\mathrm{and}\sigma =\sqrt{\frac{1}{N}\sum _i{(x_i-\mu )}^2}$

方差作为差值的平方，始终为正，而且平方将突出显示μ的异常值，并回归至平均值（如果使用绝对值而不是平方，它将回归至中位数而不是平均值）。

The variance as the square of the difference will always be positive, and squaring furthermore will highlight the outliers from μ, and regress to the mean (if an absolute value is used instead of squaring, it will regress to the median rather than to the mean).

随着试验次数趋近于无穷大，方差将趋近于零，因此在公平抛硬币的例子中，正面或反面的概率最终将趋近于平均概率 0.5，而随着试验次数趋近于无穷大，方差将趋近于零，如下图所示。

The variance will approach zero as the number of trials approaches infinity, so in the example of a fair coin toss, the probability of heads or tails will eventually proceed to the mean probability of 0.5, with a variance of zero as the number of trials approaches infinity as shown schematically in the figure below.

原子弹爆炸可以用马尔可夫链蒙特卡罗模拟 (MCMC) 进行类似模拟，因为裂变反应和中子碰撞中存在一系列可能的相互作用，这些相互作用取决于粒子弹性散射（改变方向但不改变能量）、与原子核的非弹性碰撞（改变粒子的引力场（包括电子、方向和能量）被原子核吸收，以及可能发生的原子核裂变，类似于单人纸牌游戏中牌面位置的选择。

The detonation of an atomic bomb could be similarly simulated using Markov chain Monte Carlo simulation (MCMC) because there is a domain of possible interactions in fission reactions and neutron collisions that depend on the probabilities of the particles’ elastic scattering (change direction but not energy), inelastic collisions with nuclei (change of direction and energy), absorption by the nuclei, and possible fission of the nuclei, analogous to the choice of card placement in solitaire.

举一个简单的例子，中子源穿过一个含有铀-235 的腔体，它们可能会被铀核散射或吸收，后者可能导致裂变，具体取决于中子的能量和累积的中子通量密度。因此，问题就是中子的扩散和中子的裂变倍增，其概率取决于先前得出的实验结果。中子在没有被散射或吸收的情况下行进的平均距离（平均自由程）以及中子与铀核碰撞的概率（碰撞截面）也取决于中子的动能。

As a simplified example, a source of neutrons is passing through a cavity containing uranium-235 and they may either be scattered or absorbed by the uranium nuclei with the latter possibly resulting in fission depending on the energy of the neutrons and the accumulating neutron flux density. The problem thus is one of neutron diffusion and fission multiplication of neutrons, the probabilities of which depend on previously derived experimental results. The mean distance that the neutrons will travel without being scattered or absorbed (mean free path), and the probability of a neutron collision with a uranium nucleus (collision cross-section), is also dependent on the kinetic energy of the neutrons.

众所周知（并且完全可以相信），中子在散射或吸收（自由程）之前行进距离x的概率密度P会根据原子核密度ρ及其碰撞截面ζ呈指数下降，因此，无穷小行进距离dx的无穷小概率由下式给出：

It is known (and completely believable) that the probability density P of a neutron traveling a distance x before being scattered or absorbed (free path) decreases exponentially depending on the density of nuclei ρ and their collision cross-section ζ, the infinitesimal probability for an infinitesimal travel distance dx thus is given by,

$d磷=\rho \sigma {埃}^{-\rho \varsigma 十}d十$

$dP=\rho \sigma e^{-\rho \varsigma x}dx$

对该方程进行积分将得出中子通量密度（每单位面积通过的中子数量），

Integrating this equation will give the density of the neutron flux (number of neutrons passing per unit square area) as,

$否埃你吨ronF升你十=\frac{否你米b埃rof否埃你吨rons磷\mathrm{一个}ss我n克\mathrm{电视}\mathrm{时长}ro你克\mathrm{时长}}{否你米b埃rof碳ons吨r你丙吨埃d\mathrm{电视}r\mathrm{一个}杰埃丙吨or我埃s}$

$NeutronFlux=\frac{NumberofNeutronsPassingThrough}{NumberofConstructedTrajectories}$

现在，第i次试验的自由路径长度x _i位于区间 (0, ∞) 上，可以通过进行以下变换，用计算机生成的均匀分布在区间 (0, 1) 上的伪随机数序列 ξ _{i来表示，}

Now x_i the free path length for trial i, which is over the interval (0, ∞), can be represented by a computer-generated sequence of pseudorandom numbers ξ_i uniformly distributed in the interval (0, 1) by making the transformation,

${十}_{我}=-\frac{1}{\rho \sigma }在（1-{\xi }_{我}）。$

$x_i=-\frac{1}{\rho \sigma }\ln \left(1-{\xi }_i\right).$

也就是说，通过这种变量变换，中子自由程可以用伪随机数来表示。例如，如果中子与铀同位素核碰撞的实验数据显示散射概率为 0.9，吸收概率仅为 0.1导致裂变，如果将ξ _i区间 (0, 1) 分成两组 (0, 0.1) 和 (0.1, 1)，假设计算机生成的伪随机数为 0.2，则它属于第二个较大的组 (0.1, 1)，这意味着中子已经散射。对越来越多的伪随机数组重复此操作将为上述中子通量方程提供越来越好的近似值。

That is, the neutron free path can be expressed by pseudorandom numbers through this variable transformation. For example, if experimental data for neutron collisions with uranium isotope nuclei shows a 0.9 probability of scattering and only 0.1 probability of absorption leading to fission, and if the ξ_i interval (0, 1) is segmented into two groups (0, 0.1) and (0.1, 1), if say the pseudorandom number generated by the computer for example is 0.2, then it belongs in the second larger group (0.1, 1) meaning that the neutron has been scattered. Repeating for more and more sets of pseudorandom numbers will give better and better approximations for the Neutron Flux equation above.

如果中子穿过，则赋予其“分数” s = 1，如果被吸收，则赋予其“分数” s = 0，因此对中子通量做出贡献的概率由平均分数给出$\overline{s}$其中误差用方差来衡量。

If a neutron passes through, it is given a “score” s = 1 and if absorbed s = 0, so the probability of contributing to the neutron flux is given by the mean score $\overline{s}$ where the error is measured by the variance.

对散射角进行相同类型的转换和评分，也可以模拟散射中子的方向，但还必须考虑中子散射回中子通量的可能性，这使问题变得复杂，必须在更详细的计算中加以考虑。

Performing the same type of transformation and scoring for scattering angle, the directions of the scattered neutrons can also be simulated, although the possibility of neutrons scattered back into the neutron flux must also be considered, which complicates matters and must be considered in more detailed calculations.

对于考虑质子、不同腔体设计和初始条件等的更复杂情况，可以通过先前实验得出的不同类型的反应物和腔体配置的横截面和平均自由程参数来建模，并输入到 MCMC 模拟中^。6

For more complex situations considering protons, different cavity designs and initial conditions and so on included, the situation can be modeled through previously experimentally-derived cross-section and mean free path parameters for different types of reactants and cavity configurations, and entered into the MCMC simulation.⁶

从这个例子中，可以看出中子的传播不仅仅是随机游走；也就是说，到达后续节点的步骤有不同的概率，因此只要给出相关事件的概率，就可以模拟任何由许多相互作用实体组成的系统。

From this example, it can be seen that the neutron's travels are not merely a random walk; that is, there are different probabilities for the steps taken to succeeding nodes, and so just given the relevant event probabilities, any system of many interacting entities can be simulated.

现在，从正态概率分布中抽样并运行多次 MCMC 模拟后，原子弹中子扩散通量（10 ¹⁵ –10 ^{25 ）中的大量粒子可以通过仅抽样 10 5} –10 ⁸轨迹来建模，临界质量的条件由函数f(X)表示，其中随机样本序列X _i近似于所需的概率函数^P (X)，其中f(X)与P(X)成比例。7

Now after sampling from a normal probability distribution and after many runs of the MCMC simulation, the vast number of particles in atomic bomb neutron diffusion flux (10¹⁵–10²⁵) can be modeled by sampling of only 10⁵–10⁸ trajectories, and the conditions for critical mass represented by a function f(X) with sequences of random samples X_i to approximate a desired probability function P(X), where f(X) is proportional to P(X).⁷

临界质量所需的概率P(X)可以被认为是f(X)通过马尔可夫链逐步达到的概率密度，该步骤与更大的概率相称（通常朝向随机分布的峰值），迭代地将f(X)推得更接近P(X)，并且与伯努利定律一致，MCMC 模拟总量将回归到达到铀核临界质量的平均概率，以产生足以形成自持链式反应和随后爆炸的中子扩散通量。

The desired probability P(X) for critical mass can be thought of as a probability density that is reached by f(X) stepping through the Markov chain in steps commensurate with the greater probability (generally towards the peak of a random distribution), iteratively pushing f(X) closer to P(X), and consistent with Bernoulli's law, the MCMC simulation in aggregate will regress to the mean probability of attaining a critical mass of uranium nuclei to produce a neutron diffusion flux sufficient to form a self-sustaining chain reaction and subsequent detonation.

中子穿过弹腔时，通过对参数的实验概率分布进行抽样，可以构建出大量的中子轨迹。因此，链式反应取决于整个轨迹集的总体结果。

A large number of neutron trajectories are constructed by sampling from the experimental probability distributions of parameters as the neutrons travel through the bomb cavity. The chain reaction therefore depends on the aggregate outcomes of the total set of trajectories.

^{随机分布保证了链式反应的实际概率会被105—108}条轨迹“覆盖” ，而且随着计算机计算能力的不断增强，包括用于核武器研究的超级计算机，轨迹的数量还可以不断增加，以更好地满足大数定律。

The random distribution ensures that the actual probability of a chain reaction will be “covered” by the 10⁵–10⁸ trajectories, and with the ever-increasing computational capabilities of computers, including the supercomputers used for nuclear weapons research, the number of trajectories can be increased to better satisfy the law of large numbers.

对原子弹马尔可夫链进行蒙特卡罗模拟多次将使结果的方差趋于零，从而揭示出产生原子弹爆炸所需的链式反应的平均概率。

Running the Monte Carlo simulation over the atomic bomb Markov chain many, many times will drive the variance of outcomes to zero and thereby reveal the mean probability of attainment of the chain reaction required for producing the detonation of the Bomb.

如果概率较低，则可以调整热力学和弹腔工程参数，并反复运行模拟，直到达到临界质量，并且知道临界、超临界和亚临界情况的工艺条件。

If the probability is low, then the thermodynamic and bomb cavity engineering parameters can be adjusted and the simulation run again and again until critical mass is attained and the process conditions for Critical, Super- and Sub-Critical situations are known.

了解爆炸条件至关重要，这样炸弹才能在需要的时候爆炸，而不是在实验室中爆炸，因此必须根据中子扩散的 MCMC 模拟计算出质量/能量与时间的简化图，如下图所示。

It is paramount to know the conditions for detonation so that the bomb will detonate when desired and not in the laboratory, so a simplified plot of Mass/Energy vs. Time must be calculated from the MCMC simulation of neutron diffusion, as shown in the figure below.

MCMC 的研发对于原子弹来说太晚了，但从 1951 年开始的氢弹研发需要裂变反应来产生辐射，以触发氢同位素氘和氚的聚变。

The MCMC was developed too late for the atomic bomb, but beginning in 1951 the development of the hydrogen bomb required fission reactions to generate the radiation to trigger the fusion of the hydrogen isotopes deuterium and tritium.

乌拉姆首先在约翰·冯·诺依曼的 MANIAC 计算机（源自普林斯顿大学的 IAS 计算机）上运行了针对多相互作用粒子系统的 Metropolis-Hastings MCMC 算法，后来又在宾夕法尼亚大学的 ENIAC 计算机上成功完成了模拟。

Ulam first ran the Metropolis-Hastings MCMC algorithm for a system of many interacting particles on John von Neuman's MANIAC computer (derived from the IAS computer at Princeton) and later successfully completed the simulation on the ENIAC computer at the University of Pennsylvania.

氢弹引爆的理念是基于辐射内爆，而不是仅仅利用中子通量来产生聚变，关于这是爱德华·泰勒还是斯坦尼斯拉夫·乌拉姆的提议存在争议，但泰勒对乌拉姆的马尔可夫链蒙特卡罗模拟的洞察是正确的，⁸

The H Bomb detonated based on the idea of radiation implosion instead of only neutron flux to produce fusion, with controversy over whether it was Edward Teller or Stanislaw Ulam's proposal, but Teller's insight regarding Ulam's Markov chain Monte Carlo simulations was spot-on,⁸

利用统计力学并取整体平均值，而不是遵循详细的运动学

Take advantage of the statistical mechanics and take ensemble averages instead of following detailed kinematics

总之，马尔可夫链是一组有限的连接节点，每个节点都有一个指定的选择概率，因此节点的概率分布仅取决于节点的当前状态，而不取决于过去的状态。蒙特卡罗模拟依赖于变量的转换，允许计算机生成的伪随机数表示复杂过程中的代理，大数定律确保重复试验将使系统趋于平均值，从而揭示过程的基本事实；在这个例子中，不是公平抛硬币的良性结果概率，而是原子弹或氢弹的可怕爆炸。

In summary, the Markov chain is a finite ensemble of connected nodes each having an assigned probability of choice whereby the probability distribution of nodes depends only on the present state of nodes and no past states. The Monte Carlo simulation depends on a transformation of variables allowing pseudorandom numbers generated by a computer to represent agents in a complex process, with the law of large numbers ensuring that repeated trials will drive the system to the mean, thereby revealing the ground truth of the process; in the example, instead of the benign outcome probability of a fair coin toss, the horrific detonation of an atomic or hydrogen bomb.

总统选举预测可以类比为炸弹。从普通人群中抽取的调查样本是根据党派归属、性别、经济阶层、种族等人口统计数据构建的，实际上提供了事件概率，就像中子和铀同位素核的平均自由程和碰撞截面具有散射或吸收以及随后裂变的概率一样。

An analogy with the bombs can be made for a presidential election prediction. Survey samples from the general population are constructed from demographics such as party affiliation, gender, economic class, ethnicity, and so on, providing in effect event probabilities just as the mean free path and collision cross-sections for neutrons and uranium isotope nuclei have probabilities for scattering or absorption and subsequent fission.

除了核武器和民主选举固有的风险之外，蒙特卡罗模拟还用于天气预报、喷气式飞机周围的湍流、宇宙膨胀、生物系统、生态学、股票市场和销售预测经济学以及任何运筹学问题（如交通管制和机场客流量）等更有益的领域。蒙特卡罗模拟已在几乎所有自然和社会科学和工程领域得到有效应用，尤其是在模拟人工智能大数据的结果方面。

Aside from nuclear weapons and the risks inherent in democratic elections, Monte Carlo simulation has been used in the more beneficent areas of weather prediction, turbulent airflow around jet planes, expansion of the Universe, biological systems, ecology, stock market and sales predictions economics, and in any operations research problem such as traffic control and airport passenger flow. Monte Carlo simulation has been gainfully employed in almost all science and engineering, both natural and social, and particularly in simulations of the results of the Big Data of artificial intelligence.

四结构和操作

IV Structure and Operation

我在人类中，视觉是由眼睛晶状体将光线聚焦到眼睛后部内侧的视网膜上产生的，视网膜将光线转换成电信号，眼后视神经接收电信号，通过外侧膝状体核(LGN) 中继通路将信号传输到大脑后部称为视觉皮层的神经元聚集区，如下图所示。视觉皮层接收、处理和整合视觉信号，形成一种模式，供大脑通过神经元网络进行认知处理，下图以示意图形式显示了其中一个神经元^。1

In humans, vision is generated from light focused by the eye's lens onto a retina at the inside posterior of the eye, the retina converts the light into electrical signals which are received by an optic nerve behind the eye that transmits the signals through the lateral geniculate nucleus (LGN) relay pathway to an aggregation of neurons at the posterior region of the brain called the visual cortex, as shown schematically in the figure below. The visual cortex receives, processes, and integrates the vision signals to form a pattern for the brain to cognitively process by means of a network of neurons, one neuron of which is schematically illustrated in the figure below.¹

如果来自其他皮质神经元的信号总和大于神经元树突上的信号，则皮质神经元的胞体被激活某个阈值。神经元的激活通过轴突传递到其他神经元，轴突末端与其他神经元的树突相连，根据神经科学的格言，

The soma of a cortical neuron is activated if the sum of the signals from other cortical neurons at the neuron's dendrites is greater than some threshold value. The neuron's activation is transmitted to other neurons through axons whose axon terminals are connected to the dendrites of the other neurons, and in accord with the neuroscience maxim,

一起放电、一起连接的神经元，

Neurons that Fire together, Wire together,

激活的神经元的突触放电模式在视觉皮层内形成，然后由大脑解析以形成认知图像。

synaptic firing patterns of activated neurons are formed within the visual cortex which are then resolved by the brain to form images for cognition.

在计算机视觉中，相机镜头接收物体反射的光像素，传感器阵列通过光电效应将光转换为电信号。来自人工视网膜的信号被放大，并类似于视神经和 LGN 进行中继，然后传输到仿照视觉皮层建模的人工神经网络 (ANN)。

In computer vision, a camera's lens receives pixels of light reflected from an object and an array of sensors converts the light into electric signals by means of the photoelectric effect. The signals from this artificial retina are amplified and relayed in analogy with the optic nerve and LGN, and transmitted to an artificial neural network (ANN) that is modeled after the visual cortex.

ANN 是由人工神经元阵列构成的网络。四层深度人工神经网络（各层为垂直列）的示例包括：一个输入层，用于接收网络刺激；后面是两个隐藏层；以及一个输出层；每列层有四行神经元，排列成4 × 4阵列，给定列层中的每个神经元与后续列层中的所有神经元之间都有节点连接，如下图所示。

The ANN is a network of layers of arrays of artificial neurons. An example of a four-layer deep artificial neural network (with layers being the vertical columns) has an input layer to receive stimuli to the network, followed by two succeeding hidden layers, and an output layer, each column layer having four row neurons organized in a 4 × 4 array with node connections from each neuron in a given column layer to all the neurons in the succeeding column layer, as shown in the schematic the figure below.

单个人工神经元的激活由网络中如下所示的元素表示，

The activation of an individual artificial neuron is represented by the elements in the network as designated below,

其中， ( _L )为层数，下标j表示第L层中的行神经元， ANN结构图中的yj为决策输出向量的元素。

where (L) is the layer number, the subscript j denotes the row neurons in the layer L, and the y_j in the ANN structure figure are the elements of the decisional output vector.

人工神经网络的各层以体积矩阵（二阶张量）的形式保存在计算机内存中，其中人工神经元激活级别作为元素，通常具有两个维度用于空间分布，一个维度用于颜色，以及用于决策输出的向量（一阶张量）。这些元素可以像在生物神经网络中一样以二进制方式激活为“开”或“关”，也可以像在数码相机中一样以层次方式激活，其级别反映所查看图像的光强度。

The artificial neural network's layers are held in computer memory as volume matrices (second-rank tensors) with the artificial neuron activation level as elements, typically with two dimensions for spatial distribution and one for color, and vectors (first-rank tensors) for decisional output. The elements can be binary-activated as either “on” or “off” as in the biological neural network or gradation-activated with levels reflecting the intensity of the light from the viewed image as in digital cameras.

人工智能算法是通过在ANN的矩阵层上进行基本的数学矩阵运算来执行的，这些运算包括加、减、乘、卷积、内外向量积等，体现了人工神经网络的“思考”过程，而参数化、梯度下降反向传播则实现了ANN的“学习”，其学习和识别的能力将成为其“人工智能”程度的衡量标准。

Artificial intelligence algorithms are executed by basic mathematical matrix operations on the ANN's matrix layers, including addition, subtraction, multiplication, convolution, inner and outer vector products, thus incarnating an artificial neural network's “thinking” process, while parameterization and gradient descent backpropagation effectuates the ANN's “learning”, and how well it learns and recognizes will be a measure of its “artificial intelligence”.

隐藏层的数量、大小和类型由识别任务决定。一般而言，具有两个或更多个隐藏层的人工神经网络被视为深度神经网络(DNN)。如果后续层中的所有人工神经元都与前一层中的每个神经元相连（如图所示），则称这些层是完全连接的；如果前一层中只有部分神经元与后续层相连，则它们在卷积层中形成子矩阵窗口（称为过滤器或内核），从而选择前一层的扇区以在卷积神经网络(CNN) 计算机视觉中进行特定的、更精细或更粗糙的和位置特征提取^。2

The number, size, and type of hidden layers are determined by the recognition task. Generally speaking, an artificial neural network with two or more hidden layers is considered to be a deep neural network (DNN). If all the artificial neurons in a succeeding layer are connected to each of the neurons in a preceding layer (as shown in the figure), the layers are said to be fully connected; if only some of the neurons in the preceding layer are connected to a succeeding layer, they form sub-matrix windows (called filters or kernels) in a convolutional layer whereby sectors of a preceding layer are selected for specific, finer or coarser, and positional feature extraction in convolutional neural network (CNN) computer vision.²

在前馈模式下，激活的神经元将网络中后续人工神经元中的人工神经元连接起来，形成人工神经元激活的突触模式，就像在生物神经网络中一样。然而，在人工神经网络中，每个人工神经元的激活水平对形成模式的重要性都是通过加权和偏置激活来人为调节的，这个过程称为参数化，有助于区分模式的特征^。3

In feedforward mode, the activated neurons connect the artificial neurons in succeeding artificial neurons in the network to form synaptic patterns of artificial neuron activation, just as in a biological neural network. However, in an artificial neural network the importance of each artificial neuron's activation level towards forming a pattern is artificially modulated by weighting and biasing the activations in a procedure called parameterization that helps to distinguish the features of the pattern.³

权重和偏差最初是任意分配的，为人工神经网络形成了一个空白画布，通过增强重要特征和减少不重要特征（如噪声或背景）来感知模式。在监督学习中，ANN 会获得一个标记的训练数据集，它会尝试通过调整权重和偏差的初始随机值来匹配数据集，以通过梯度下降并通过其网络层反向传播该误差来最小化其激活模式和标记训练数据集之间的差异（误差） 。当误差接近于零（收敛）时，训练集数据的显著特征已被学习，可用于未来的识别任务。

The weights and biases are initially arbitrarily assigned, forming a blank canvas for the artificial neural network to perceive patterns by enhancement of significant features and diminution of insignificant ones (such as noise or background). In supervised learning, the ANN is presented with a labeled training dataset, it attempts to match the dataset by adjusting the initially random values of the weights and biases to minimize the difference (error) between its activation pattern and the labeled training dataset by gradient descent and backpropagating that error through its network layers. When the error approaches zero (converges), the distinguishing features of the training set data has been learned, to be used for future recognition tasks.

一般来说，第一个隐藏层从神经元激活水平的明显变化中检测“高级”特征，如边缘，例如猫耳朵的三角形边缘，第二个隐藏层检测“低级特征”，如毛皮的颜色，后续层在分层特征提取过程中挑选或细化毛皮中的图案等特征。通过参数调整来描绘特征，以最小化与训练集的误差，组合结果将提供猫的特征，以供存储以供以后识别所看到的物体。

Generally, the first hidden layer detects “high-level” features such as edges from clear shifts in neuron activation level, for example the triangular edges of a cat's ears, the second hidden layer detects “low-level features” such as the color of fur, and succeeding layers pick out or refine features like patterns in the fur in a process of hierarchical feature extraction. After delineating the features by parameter adjustment commensurate with minimizing the error with the training set, the combined result will provide characteristic features of a cat to be stored for later recognition of viewed objects.

添加更多隐藏层并采用卷积层进行更精细的特征提取和相对定位，应该会产生更精细的复合特征阵列，但额外的层当然会带来更大的计算负担。

Adding more hidden layers and employing convolutional layers for finer feature extraction and relative position should result in a more refined composite array of features, but additional layers of course carry a greater computational burden.

有许多超参数可以添加和调整，以微调人工神经网络的识别能力，并且可以对反向传播梯度下降进行超参数化，以获得更高的稳定性和收敛速度^。4

There are many hyperparameters that can be added and adjusted to fine-tune the artificial neural network's recognition capability, and the backpropagation gradient descent can be hyperparameterized for greater stability and speed of convergence.⁴

经过监督训练后，如果 ANN 想要下棋、围棋或玩视频游戏，它可以进一步进行强化学习(RL)，其中根据 ANN 在游戏中的动作是否有助于达到与成功相称的目标来给予奖励和惩罚。

After the supervised training, if the ANN wants to play chess, Go, or video games, it can further undergo reinforcement learning (RL) wherein rewards and punishments are given based on the ANN's moves in the games being helpful or unhelpful in reaching a goal commensurate with success.

深度信念神经网络( DBN) 为 ANN 提供概率分布，而不是对象或数据，根据 ANN 可能试图确定的概率为ANN 提供先验信念。例如，在自动语音识别中，隐马尔可夫模型采用马尔可夫链提供统计概率来推断字母、单词或语音序列，这些字母、单词或语音序列的出现概率高于其他字母、单词或语音序列，例如在辅音之后出现元音和修辞手法的情况下。

A deep belief neural network (DBN) fuels the ANN probability distributions rather than objects or data, providing the ANN with a prior belief based on those probabilities about which it may be trying to ascertain. For example, in automatic speech recognition, a Hidden Markov Model employs a Markov chain to provide statistical probabilities to infer letters, words, or speech sequences whose occurrences are more probable than others, in cases such as vowels after consonants and figures of speech.

由于语音识别不仅在很大程度上依赖于声学模式，还依赖于话语的时间，因此循环神经网络(RNN) 会延迟、激活或停用选定的人工神经元，以对语音进行时间表征并根据先前的语音模式识别推断（循环）。

Since speech recognition is strongly dependent not only on acoustic patterns, but also on the timing of utterances, a recurrent neural network (RNN) delays, activates, or deactivates selected artificial neurons for temporal characterization of the speech and for identifying inferences based on prior patterns of speech (recurrence).

在无监督学习中，ANN 从头开始​​学习，通过针对自身的不同改进版本进行训练，自下而上地自我强化，最终发展成为纯粹的推理引擎，例如 AlphaGoZero，它在国际象棋、围棋和视频游戏中击败了人类冠军，而无需事先了解游戏规则，并且能够直接从实际语音中学习模式和语音识别，而无需监督训练。

In unsupervised learning, the ANN learns from scratch by training against different improving versions of itself in a process of self-strengthening from the bottom up to ultimately develop into a pure-play inference engine such as AlphaGoZero which dominated human champions in chess, Go, and video games without a priori knowing the rules of the games, and is capable of learning pattern and speech recognition directly from actual speech without supervised training.

所有这些不同类型的人工神经网络、参数化、梯度下降、反向传播和超参数化将在后面的章节中更详细地描述。

All of these different types of artificial neural networks, the parameterization, gradient descent, backpropagation, and hyperparameterization will be described in more detail in the following chapters.

一个孩子第一次看到猫，父母告诉她猫叫什么名字时，她会想象出猫的形象，其主要特征是毛皮、四条腿、长尾巴、尖耳朵、大圆眼睛、胡须和小粉红三角形鼻子，所有这些都以吸引人的方式排列。孩子的视觉皮层形成复合图像，将其标记为“猫”，并将其存储在记忆中。

A child upon seeing a cat for the first time, and being told by her parents what it is called, creates an image with the prime features of fur, four legs, a long tail, pointy ears, big round eyes, whiskers, and a small pink triangular nose, all arranged in an appealing configuration. The child's visual cortex forms the compound image, labeling it as a “cat” and stores it in memory.

在计算机视觉中，物体反射的光被相机镜头拾取，并通过类似视神经的中继器传输到类似视网膜的光电探测器，后者将光转换为成比例的电信号。然后，这些信号通过定期采样信号并为每个样本分配一个代表亮度级别的数字（范围从 0 到 1）进行模拟到数字转换，称为灰度，用于将数字输入到像素阵列中。

In computer vision, light reflected from an object is picked up by a camera's lens and transmitted through an optic nerve-like relay to retina-like photodetectors that convert light to proportional electrical signals. Those signals are then analog-to-digital converted by sampling the signals at regular intervals and assigning each sample a number representing the level of brightness in a range from 0 to 1, called greyscale for digital entry into an array of pixels.

像素阵列在计算机中表示为具有不同光强度的像素的二维矩阵，其中第三维包含原色，通常是红、绿、蓝 (RGB)，它们按比例组合在一起可以产生任何颜色，就像电视摄像机在液晶显示器 (LCD) 屏幕上重现图像一样。

The array of pixels is represented in a computer as a two-dimensional matrix of pixels of different light intensity with a third dimension holding the primary colors typically red, green, blue (RGB) in proportions that can together generate any color, much like a television camera does in reproducing images on a liquid crystal display (LCD) screen.

然而，计算机视觉不仅仅是重现物体的图像以供观看，计算机的三维体积矩阵类似于人类的视觉皮层，构成了一个人工神经网络（ANN），可以通过人工神经元突触连接模式形成和存储物体的特征图，就像生物视觉皮层形成心理图像一样。

Computer vision, however, does more than just reproduce an image of the object for viewing, the computer's three-dimensional volume matrix, in analogy with the human visual cortex, constitutes an artificial neural network (ANN) that can form and store feature maps of objects by artificial neuron synaptic connection patterns just like the biological visual cortex forms a mental image.

然后，ANN 就像一个孩子学习识别物体一样，可以在标记数据集上进行监督训练。通过调整应用于人工神经元亮度水平的权重和偏差参数，使之更接近训练集亮度水平模式，从而最大限度地减少 ANN 的突触模式与训练数据集之间的差异，迭代减少人工神经网络层中的“误差”，以创建所观察物体的突触模式特征图，并将其存储和标记在 ANN 的内存中，以供后续识别。

ANN then, just like a child learning to recognize objects, can undergo supervised training on labeled datasets. The difference between ANN's synaptic patterns and the training dataset is minimized by adjusting weight and bias parameters applied to the artificial neuron brightness levels to more closely match the training set brightness level patterns, iteratively reducing the “error” in the artificial neural network layers to create synaptic pattern feature maps of the viewed object to be stored and labeled in ANN's memory for subsequent recognition.

在分类模式识别中，当一个物体被提交给 ANN 进行识别时，ANN 的标记特征图会与所查看的物体进行比较，然后对该物体进行分类。在聚类模式识别中，未标记的数据被提交给 ANN，然后 ANN 根据特征相似性对数据进行分组。

In classification pattern recognition, when an object is presented to ANN for recognition, ANN's labeled feature maps are compared with the viewed object and the object is classified. In clustering pattern recognition, unlabeled data is presented to ANN, who then groups the data in accord with feature similarities.

数据可以用向量表示，其分量是大小、形状、颜色等特征，其“接近度”由不同向量的内积（点积）决定。大多数模式识别算法都是基于统计推断进行“识别”，输出层列出了特定特征的识别概率。

The data can be represented by vectors with the components being the features such as size, shape, color, and so on, and their “closeness” determined by the inner (dot)product of different vectors. Most pattern recognition algorithms “recognize” based on statistical inference, and output layers list the probabilities of the recognition of specific features.

标记模板识别可用于识别相对简单、定义明确的整体对象，例如印刷的数字和字母表的字母，以及机器人组装的明确指定的组成部分，但即使只有轻微差异的对象也可能无法使用模板进行准确分类。

Labeled template recognition can be used for identifying relatively simple, well-defined whole objects, such as printed digits and letters of the alphabet, and clearly specified component parts for robotic assembly, but objects that are even only slightly different may not be classified accurately using templates.

对于更复杂的物体和场景的模式识别，边缘最容易检测，因为它们是从背景到物体的突然灰度变化，例如猫的耳朵；同样，对于突然的颜色变化，如躺在蓝色地毯上的橙色猫。

For pattern recognition of more complicated objects and scenes, edges are easiest to detect as they are an abrupt greyscale change in transitioning from the background to the object, for example a cat's ears; likewise for abrupt color changes like an orange cat lying on a blue rug.

然而，即使是突然的变化也可能被识别系统中纹理变化、划痕或电子不稳定等形式的噪声所掩盖。可以通过将像素亮度值替换为其自身及其相邻像素的平均值或中值来平滑此类噪声，从而消除噪声但保留对比度。

However, even abrupt changes can be obscured by noise in the form of variations in texture, scratches or electronic instability in the recognition system. Such noise can be smoothed by replacing the pixel brightness value with the average or median of itself and its neighbors, thus eliminating the noise but preserving the contrast.

深度感知是通过两个独立的相机进行立体成像而获得的，但这需要将每个探测器图像的对应点关联起来。这可以通过将灰度阵列简化为边缘图、扫描图以查找相似的外观以识别对应点、然后测量到每个相机图像平面的距离，并根据这些差异逐点重建三维图像来实现。

Depth perception is gained by two separated cameras for stereographic imaging, but this requires correlation of the corresponding points of each detector's image. This can be done by reducing the greyscale arrays to edge maps, scanning the maps for similar appearances to identify the corresponding points, then measuring the distance to each camera's image plane, and from those differences, reconstructing a three-dimensional image point-by-point.

这个过程看似非常复杂，需要对图像中的每个像素几乎立即进行多次计算，但这正是计算机所能做的，在这种情况下几乎与两只生物眼睛一样好。

A seemingly very involved process requiring almost instantaneous multiple computations for every pixel in an image, but this is just what a computer can do, in this case almost as well as two biological eyes.

识别的一个重要特征是物体的纹理；即像素亮度的规则模式，例如玉米粒中的标记（显著特征）的结构分析，以及猫毛等方向一致性的统计分析。通过像素强度级别与其邻近像素强度级别相似的统计概率，可以相对容易地检测标记和一致性。

An important feature for recognition is an object's texture; that is, regular patterns of pixel brightness, such as the structural analysis of tokens (salient features) like kernels in an ear of corn, and statistical analysis of directional coherence like a cat's fur. Tokens and coherence can be relatively easy to detect by means of the statistical probability that a pixel's intensity level will be similar to that of its near neighbors.

相机只需要三原色（ “原色”是指三原色中没有一种颜色可以通过其他两种颜色混合而成），通常是红、绿、蓝 (RGB)，因为每种原色的成分混合都可以产生任何颜色。这可以用一个简单的方程来表示，

A camera needs only three primary colors (“primary” meaning no one color of the primary three can be made from mixtures of the other two), typically red, green, and blue (RGB), because the admixture of components of each primary color can produce any color. This can be represented by a simple equation,

其中r、g和b是每种原色的分量。因此，在具有红、绿、蓝轴的三维坐标系中，任何颜色都可以用其 RGB 分量的值表示为3D 颜色空间中的点。

where r, g, and b are the component amounts of each primary color. So in a three-dimensional coordinate system with red, green, and blue axes, any color can be represented by a point in the 3D color space from the value of its RGB components.

颜色识别的主要困难之一是，其三个独立属性，色调、强度和饱和度，主要取决于物体的照明类型、角度和强度。要识别色调，计算机视觉必须首先确定强度和饱和度；强度可以取为三个 RGB 强度值的平均值，饱和度是颜色与照明的比率，但在不同的照明条件下，计算机视觉中准确区分颜色可能仍然很困难^。1

One of the main difficulties of color recognition is that its three independent attributes, hue, intensity, and saturation, depend critically on the type, angle, and intensity of illumination on the object. To recognize hue, computer vision must first determine the intensity and saturation; the intensity can be taken as the average of the three RGB intensity values and the saturation is the ratio of color to illumination, however the accurate distinction of colors in computer vision may still be difficult under different lighting conditions.¹

可以提取形状、纹理和颜色的组合（称为特征）来进行分类，例如，仅基于它们的不同形状和颜色对一篮水果中的草莓和香蕉进行分类，但将草莓与西红柿区分开来则需要尺寸尺度和纹理分析。

Combinations of shape, texture, and color called features can be extracted for classification of, for example, strawberries and bananas in a basket of fruits based solely on their different shape and color, but separating strawberries from tomatoes would require size scale and texture analysis.

对于更复杂的物体，必须利用结构关系进行识别，例如腿、尾巴、尖耳朵、毛皮、大圆眼睛，并且三角形的鼻子必须能够被识别为一只猫，但是不同的姿势，比如安详地坐着和双腿叉腰仰卧，仍然必须被归类为一只猫。

For more complex objects, structural relationships must be employed for recognition, for example the legs, tail, pointy ears, fur, big round eyes, and triangular nose must be to be identified as a cat, but different poses, such as sitting serenely and lying on its back with legs akimbo, must still be classified as a cat.

假设向人工神经网络展示了一只可爱的橙色短毛小狗，但是它的训练集中，在狗分类中主要由大丹犬和德国牧羊犬等大型犬组成，而它的猫分类包括许多可爱的橙色短毛小猫，那么 ANN 很可能会把狗误认为是猫。

Suppose an artificial neural network was presented with a cute little orange shorthair puppy, but its training set, in the dog classification primarily consisted of large dogs such as great danes and German shepherds, and its cat classification included many cute small orange shorthair kittens, then ANN may well misidentify the dog as a cat.

如果经过多次训练来扩大和细化狗的特征图之后，我们的小狗仍然被误认为是一只猫，那么 ANN 就有责任在小狗训练集上进行更多的监督学习。

If after many more training runs to enlarge and refine the dog feature maps, our puppy is still misidentified as a cat, it will be incumbent on ANN to undergo more supervised learning on puppy dog training sets.

或者，ANN 可以重新校准猫的特征图来强调明显可区分的差异，例如猫的粉红色鼻子与狗的黑色鼻子形成对比，因此鼻子的第三维颜色矩阵元素粉红色应该具有更大的权重，或者为猫手工设计粉红色鼻子颜色偏差。

Alternatively, ANN could recalibrate the cat feature maps to emphasize the apparently distinguishable differences, for example a cat's pink nose as opposed to a dog's black none, so the third dimension color matrix element pink for the nose should be more heavily weighted or a pink nose-color bias hand-engineered for cats.

通过更多的训练集，包括长得像狗的垂耳苏格兰折耳猫和长得像猫的萨摩耶犬，再加上使用手工设计的权重和偏差（比如对猫的粉红色鼻子有更大的偏差）进行更多的训练周期，然后就可以逐步做出更细致的区分，ANN 将能够更好地对猫和狗进行分类。

By more training sets including say dog lookalike floppy-eared Scottish Fold cats and cat lookalike Samoyed dogs, plus more training epochs with hand-engineered weights and biases (for example a greater bias towards cats in response to their pink noses, then progressively finer distinctions can be made, and ANN will be better able to classify dogs and cats.

电视人工神经网络中的隐藏层通过从一层到下一层的前馈人工神经元激活来联合提取独特特征，从而实现分层特征提取。在生物视觉系统中，皮质神经元被认为是二元激活（开/关），只有高于某个阈值的激活水平才会引发与其他神经元的突触连接。在人工神经网络中，初始激活水平可以与输入信号强度成比例，提供缩放信息，但激活水平通常是随机选择的，提供空白画布，当通过参数化进行调制时，可以更好地反映训练集数据。

The hidden layers in an artificial neural network conjunctively extract distinctive features by feedforward artificial neuron activation from one layer to the next for hierarchical feature extraction. In biological vision systems, cortical neurons are believed to be binary activated (on/off) and only activation levels above some threshold will instigate a synaptic connection to other neurons. In artificial neural networks, the initial activation levels can be proportional to the input signal intensity, providing scaled information, but the activation levels usually are randomly selected, providing a blank canvas that when modulated by parameterization, better reflects the training set data.

参数化通过增强人工神经元激活水平，或者相反，通过将激活水平乘以加权因子并在给定层中的激活水平总和中添加偏差，降低难以区分的神经元激活水平，为区别性特征提供了更大的意义。

Parameterization provides greater significance to distinctive features by enhancing artificial neuron activation levels, or conversely diminishing the indistinguishing neuron activation levels, by multiplying the activation level by a weighting factor and adding a bias to the sum of activation levels in a given layer.

感知器是一种人工神经元，它接受多个二进制（0或1）输入x _i并产生单个二进制输出a（是= 1 或否= 0）。每个x _i输入都乘以反映该输入重要性的权重w _i，将加权输入相加，如果加权和小于或大于或等于某个选定的阈值偏差b ，则做出激活（是）或不激活（否）的决定a，如示意图^1所示

A perceptron is an artificial neuron that takes multiple binary (0 or 1) inputs x_i and produces a single binary output a (Yes = 1 or No = 0). Each x_i input is multiplied by a weight w_i reflecting the significance of that input, the weighted inputs are summed, and if the weighted sum is less than or greater or equal to some chosen threshold bias b, the decision a to activate (yes) or not (no) is made, as illustrated by the schematic figure,¹

例如，你正在决定是否参加钢琴演奏会；虽然有几个决策因素，但这是一个二元决策，是或否。假设输入因素为：

For example, you are trying to decide whether to attend a piano recital; there are a few decisional factors but it is a binary decision, yes or no. Say the input factors are:

x ₁ =距离较近，可以步行，

x ₂ =女朋友和你一起去，

x ₃ =女朋友的弟弟也来了。

x₁ = close by so can walk,

x₂ = girlfriend goes with you,

x₃ = girlfriend's little brother comes too.

你分析了一下情况：你喜欢钢琴音乐，演奏会就在附近，你认为你的女朋友想和你一起去，但她可能会带她的弟弟一起去。在这种情况下，你还想去吗？有哪个因素起决定作用？如果没有，那么就需要更深入的分析。

You analyze the situation: You like piano music, the recital is close by, and you think your girlfriend would like to go with you, but she may bring her little brother along. In that case do you still want to go? Is any one factor decisive? If not, then a deeper analysis is required.

可以通过为每项输入因素赋予权重来确定其相对重要性；例如，没有车、钱不多，步行距离内很重要，因此w ₁ = 3；你的女朋友来参加非常重要，因此w ₂ = 5；但她的弟弟也来参加绝对是负面的，因此w ₃ = –4。你喜欢钢琴音乐，因此参加的门槛很低（出于偏见）b = 6。

The relative importance of each input factor can be determined by attaching a weight to it; for instance, having no car and little money, within walking distance is important, so w₁ = 3, your girlfriend coming is very important, so w₂ = 5, but her little brother also coming is a definite negative, so w₃ = –4. You like piano music so the threshold for attending is a low (for biases) b = 6.

因此，如果您可以步行去听音乐会，而您的女朋友会不带她的弟弟一起去，则加权和为1 × 3 + 1 × 5 + 0 × (–4) = 8 > 6，因此决策是去，您可以只和她一起步行去听演奏会。如果她（可能还有她的弟弟）不和您一起去，那么即使您可以步行去听演奏会，您也不会去，因为1 × 3 + 0 × 5 + 0 × (–4) = 3低于阈值。如果她会去但会带她的弟弟，那么您的决定会更加困难，但感知器会为您决定。加权和为1 × 3 + 1 × 5 + 1 × (–4) = 4 < 6，因此如果她的弟弟一起去，您就不会去。

Therefore, if you can walk to the concert and your girlfriend will come without her little brother, the weighted sum is 1 × 3 + 1 × 5 + 0 × (–4) = 8 > 6, and so the decision will be to go, you can walk with only her to the recital. If she (and presumably her little brother) will not come with you, then you won’t go even if you can walk to the recital since 1 × 3 + 0 × 5 + 0 × (–4) = 3 is below the threshold. If she will go but brings her little brother, your decision is more difficult, but the perceptron will decide for you. The weighted sum is 1 × 3 + 1 × 5 + 1 × (–4) = 4 < 6, so you will not go if her little brother comes along.

参数化显然有助于决策，但感知器也确定了一个关键因素，即小兄弟。通过找到一些基本事实，可以帮助你做出决定，例如，如果（希望）小哥哥那天晚上要上小提琴课。最糟糕的情况当然是你的女朋友不和你一起去，但她的弟弟会去，你就得付 Uber 的车费，而且演奏会上演奏的曲子都是无调性的。

Parameterization clearly helps decision-making, but the perceptron has also identified a critical factor, namely little brother. Your decision can be helped along by finding some ground truth, for instance if (hopefully) little brother has violin lessons that night. The worst case is of course your girlfriend does not come with you, but her little brother does, you have to pay for an Uber ride, and the pieces played at the recital are all atonal.

有趣的是，除了帮你决定是否去之外，感知器还揭示出一个推论：钢琴音乐对你来说可能并不那么重要；也就是说，你女朋友无拘无束的伴奏可能比你的任何文化自负都更重要。

Interestingly, in addition to deciding for you whether to go or not, the perceptron also reveals an inference that piano music may not be all that important to you; that is, your girlfriend's unfettered accompaniment is likely more important than any cultural pretensions you may have.

如果你发现音乐会上有你特别喜欢的作曲家的作品，你就可以降低参加的门槛，也就是参加的几率会增加，甚至小弟弟跟着去也值得。

If you find out that the recital will have pieces by composers that you particularly like, you can lower the threshold towards attending; that is, the bias towards attending is increased, perhaps even to the extent of little brother tagging along being worth it.

因此，感知器是一种复杂的决策装置，通过分配权重来操作，这些权重表示决策因素的相对正面和负面重要性，并使用阈值偏差来反映决策的重要性。

The perceptron therefore is a sophisticated decision-making device operated by assigning weights that signify the relative positive and negative significance of decisional factors, with a threshold bias reflecting the importance of the decision.

人工神经网络中的这种参数化是通过将人工神经元层视为感知器、加权每个神经元的激活水平并偏置层中的总和来增强或减弱该神经元层对后续层神经元激活的影响来实现的，最终在网络中形成代表训练集数据特征的突触模式。

This kind of parameterization in artificial neural networks is done by treating the artificial neuron layer as a perceptron, weighting each neuron's activation level and biasing the sum in a layer to enhance or diminish the effect of that neuron layer on the activation of the succeeding layer's neurons to ultimately form synaptic patterns in the network representing features in the training set data.

在上面的感知器例子中，权重和偏差是根据个人的偏好分配的，但是，一个表面上没有偏好的机器如何针对任何特定情况确定权重和偏差呢？

In the perceptron example above, the weights and biases were assigned according to an individual's preferences, but just how are the weights and biases determined for any given situation by a machine which ostensibly has no preferences?

权重的初始值可以任意指定，因为它们将通过参数化进行调整，参数化将迭代调整权重的值以匹配标记的训练数据集，从而构成学习过程。初始化时通常使用正态（高斯）分布的随机值，以避免由于初始权重相同而导致后续学习到的不同对象相似。

The initial values of the weights can be arbitrarily assigned because they will be tuned by a parameterization that will iteratively adjust the values of the weights for matching a labeled training data set, thereby constituting a learning process. Random values of a Normal (Gaussian) distribution are typically used in initialization so as to avoid subsequent learning of different objects being similar because of the same initial weightings.

从数学上描述，网络层 (0) 中所有神经元的加权激活水平都连接到人工神经网络的后续层 (1) 中的每个神经元，并通过权重进行调制；例如，后续层 (1) 中第0^个神经元的激活由第ⁱ行和^第j层权重w _{i,j乘以前一个}^第0层的j 个神经元的激活水平之和给出，²

Described mathematically, the weighted activation levels of all the neurons in layer (0) of the network are connected to every neuron in the succeeding layer (1) of the artificial neural network and modulated by weights; for example, the activation of the 0^th neuron in the succeeding layer (1) is given by the sum of the i^th row and j^th layer weights w_i,j times the activation levels of the preceding 0^th layer's j neurons,²

因此，权重就像网络中相邻层神经元之间连接强度的度量。因此，可以看出，输入层中的第一个突触连接强度模式完全基于随机激活水平，通过调整权重和偏差来细化，以最小化与训练集数据的差异。隐藏层分层特征提取将进一步将特征与其周围环境相吻合。

The weights thus are like a measure of the strength of the connections between the neurons in adjacent layers in the network. As such, it can be seen that the first synaptic connection strength pattern in the input layer, based solely on random activation levels are refined by adjusting the weights and biases in accord with minimization of differences with the training set data. Hidden layer hierarchical feature extraction will further dovetail the characteristic features and their surroundings.

为了进一步提高图像特征的辨别能力，可以在加权激活水平的总和中添加不同的偏差（_b0），例如正偏差以确保神经元层中的加权和对不同特征的特征提取有有意义的贡献，或者相反，负偏差可以淡化或完全忽略不相关的特征和噪声，

To further improve image feature discrimination capability, different biases (b₀), can be added to the sum of weighted activation levels, for instance positive biases to ensure that the weighted sum in a neuron layer will meaningfully contribute to the feature extraction of distinct features, or conversely negative biases to downplay or totally ignore irrelevant features and noise,

光学显示器不使用生物皮层神经元的二进制“开”（1）或“关”（0）或区间（0，∞）内光强度的无限线性增加，而是使用 0 到 1 之间的十进制灰度值来表示激活强度。由于范围内的小数可以无限小，因此人工神经元激活水平可以非常精细但仍然可以区分（尤其是通过计算机）。此外，权重和偏差的微小变化将正确地在特征图中产生微小变化，并且不会无意中导致梯度下降中的导数以显着性反转翻转，加权和和偏差的较大变化也不会导致梯度下降反向传播发散。

Instead of the binary “on” (1) or “off” (0) of biological cortical neurons or the unlimited linear increase of light intensity in the interval (0, ∞), optical displays use a greyscale of decimal values between 0 and 1 for activation intensities. Because the decimal fractions within a range can be infinitesimally small, the artificial neuron activation level can be extremely fine yet still distinguishable (particularly by a computer). Furthermore, small changes in weights and biases will properly produce small changes in the feature maps, and will not inadvertently cause the derivatives in gradient descent to flip in reversals of significance, nor will large changes in weighted sums and biases cause the gradient descent backpropagation to diverge.

灰度由S 型函数（也称为逻辑函数）生成，该函数将变量x限制在域 (0, 1) 内，以在渐近 1 和 0 之间产生可数无限个可能值，

Greyscale is generated by the sigmoid function (also called the logistic function) that restricts variables x to the domain (0, 1) to produce a countably infinite number of possible values between the asymptotic 1 and 0,

为了表达模式识别中使用的概率，S 型函数输出必须为正，因为不存在负概率；因此，由于指数函数e没有负值，因此它非常适合提供正灰度值^。3

To express the probabilities used in pattern recognition, the sigmoid function output must be positive because there is no such thing as a negative probability; so since the exponential function e has no negative values, it is ideally suited to provide positive greyscale values.³

S 型函数还可以表示阶跃函数的平滑版本，因此它也可以区分“是/否”，具体取决于x的值为负数还是正数，如上图中σ(x)的图所示，因此可以将对象分离到图的左侧和右侧，因此可以用于对象分类，例如区分猫和狗、相关电子邮件和垃圾邮件，以及在社交网络中对嘻哈音乐和古典音乐爱好者进行分类。

The sigmoid function can also represent a smoothed version of a step function, so it can also “Yes/No” differentiate, depending on the value of x as either negative or positive as can be seen by the plot of σ(x) in the figure above, and thus objects can be separated into the left and right sides of the graph, and so can be used for object classification, such as distinguishing cats from dogs, germane from spam emails, and classifying hip-hop and classical music aficionados in social networks.

一层中一个神经元的 S 型函数对神经元激活水平权重和偏差进行如下操作：

The sigmoid function for one neuron in one layer operates on the neuron activation level weights and biases as

神经网络的每一层都有多个神经元，因此从前一层的神经元接收突触灰度激活的给定神经元本身具有激活水平，该激活水平可以通过权重矩阵乘以前一层神经元激活水平向量，再加上偏差向量，然后由 S 型函数对整个套件进行操作来表示。

There are multiple neurons in each layer of a neural network, so a given neuron receiving synaptic greyscale activation from a preceding layer's neurons itself has an activation level that can be represented by a multiplication of a weights matrix times the preceding layer neuron activation level vector, plus the bias vector, and then the whole kit operated on by the sigmoid function.

例如，在我们的简单4×4神经网络中，矩阵形式中第 (1) 层神经元的灰度激活水平作为第 (0) 层神经元激活水平的函数，由下式给出：

For example, the greyscale activation levels for the neurons in layer (1) as a function of the neuron activation levels of layer (0) in our simple 4 × 4 neural network in matrix form is given by,

其中a ^{(1)是一个列向量，表示}第 1层的所有加权神经元激活水平，用权重矩阵的 S 型函数乘以前一层的神经元激活水平加上每个加权向量和的偏差来表示。该方程可以简洁地写成：

where a⁽¹⁾ is a column vector representing all the weighted neuron activation levels in layer 1 expressed in terms of the sigmoid function of the weights matrix times the previous layer's neuron activation levels plus the biases for each weighted vector sum. The equation then can be written compactly as,

其中W是加权矩阵，b是层 (0) 中偏差的列向量，sigmoid 函数对向量Wa ⁽⁰⁾ + b ⁽⁰⁾进行运算，产生第 1 层神经元的加权灰度激活a ^(1)。这个优雅的方程明确地显示了后续层神经元激活对前一层所有神经元的加权神经元激活水平及其偏差的依赖关系。

where W is the weighting matrix, and b is a column vector of biases in layer (0), with the sigmoid function operating on the vector Wa⁽⁰⁾ + b⁽⁰⁾ to produce the weighted greyscale activation a⁽¹⁾ of the neurons in layer 1. This elegant equation explicitly shows the dependence of succeeding layer neuron activations on the weighted neuron activation levels and their biases of all the neurons in the preceding layer.

从这个角度看，每个神经元层都是一个感知器，排列在一个多层网络中，这个网络恰如其分地被称为多层感知器(MLP) 模型，这是最早的现代人工神经网络。每个神经元都有一个输入，该输入由来自前一层的加权和偏置神经元激活水平以及它自己的合成激活水平组成，该合成激活水平随后将通过权重和偏置进行调制，以所谓的前馈模式输入到下一层的神经元中。

Seen in this way, each neuron layer is a perceptron arrayed in a multilayered network called appropriately enough a Multilayer Perceptron (MLP) model, the earliest modern artificial neural network. Each neuron has an input comprised of the weighted and biased neuron activation levels from the preceding layer, and a resultant activation of its own, which will be subsequently modulated by weights and biases for input to the neurons in the next succeeding layer in the so-called feedforward mode.

就 S 型函数而言，第 (1) 层神经元的激活为：

The activation of layer (1) neurons in terms of the sigmoid function is,

然后，必须像上述那样处理每一层神经元的激活，并且由于人工神经网络可能具有许多层和神经元，以及大量的训练集数据，尽管计算负担很重，但这种网络是非常可编程的，因为计算机非常擅长矩阵的线性代数，并且使用可以同时计算矩阵运算的大规模并行图形处理单元（GPU），计算速度很快。

The activation of every layer's neurons then must be processed as above, and since artificial neural networks may have many layers and neurons, together with voluminous training set data, even though computationally burdensome, such a network is eminently programmable because computers are very good at the linear algebra of matrices, and computations are fast using massively-parallel graphical processing units (GPUs) which can compute the matrix operations simultaneously.

如此艰巨的计算表明了为什么人工智能直到大容量存储、超高速并行处理计算机的出现，以及利用这些硬件的高效学习和识别算法的诞生才得以真正腾飞。

Such daunting calculations show why artificial intelligence could not really take off until the advent of mass-storage, ultra-fast parallel-processing computers, and the creation of efficient learning and recognition algorithms taking advantage of that hardware.

除了由此而产生的新硬件和创新的学习算法之外，人工智能还通过MatLab、Octave和Numpy等免费开源计算软件， ImageNet等可以自由获取的训练集，以及GitHub和RedHat等免费公开使用和包容性系统开发的主机编码平台得到了更迅速、更全面的发展，所有这些都可以通过互联网方便地供任何人使用。

In addition to the new hardware and innovative learning algorithms made possible thereby, artificial intelligence has been developed more rapidly and comprehensively by free open source computational software from MatLab, Octave, and Numpy, freely accessible training sets such as ImageNet, and the free public use and inclusive system development of host-computer coding platforms such as GitHub and RedHat, all conveniently available to anyone on the Internet.

随着21^世纪人工智能资源的去中心化（民主化）和共享化（社区化），人工智能在经历了20世纪90年代的“人工智能寒冬”之后，得以迅速、广泛地蓬勃发展。

With the 21^st Century's decentralization (democratization) and sharing (communization) of artificial intelligence resources, rapid widespread AI development could proceed vigorously after the AI Winter of the 1990s.

早期的 AI 系统中通常使用S 型函数和双曲正切函数 ( tanh )，但最近开发的系统使用更简单的整流线性单元( ReLU ) 函数，其定义为：

The sigmoid function and the hyperbolic tangent function (tanh) were commonly used in early AI systems, but more recently-developed systems use the simpler Rectified Linear Unit (ReLU) function defined as,

这只是一条45^度直线，将所有负激活值更改为0，并在网络中使用softmax函数，将提供灰度。这个简单的函数显然比 sigmoid 和双曲正切更容易计算，因此处理速度更快，同时与其他灰度函数相比，准确度没有显著差异。

which is just a straight 45^o line that changes all the negative activations to 0, and with a softmax function in the network, will provide greyscale. This simple function is obviously easier to compute than sigmoid and hyperbolic tangent and therefore faster to process while making no significant differences in accuracy compared to other greyscale functions.

此外，由于当 sigmoid 和 tanh 神经元激活水平输出接近0或1时，学习梯度趋近于零，因此学习将严重减慢或停止（饱和）。开放式 ReLU 神经元不会饱和，因此学习不会减慢，但是如果 ReLU 神经元的最终加权输入为负，则梯度消失（趋近于零），因此 ReLU 神经元也将停止学习总的来说。这些缺陷催生了大量的替代灰度转换函数，可以根据特定 AI 任务的需要临时使用^。4

Furthermore, since the learning gradient approaches zero when the sigmoid and tanh neurons activation level outputs are near either 0 or 1, learning will severely slow down or stop (saturate). An open-ended ReLU neuron will not saturate, so the learning will not slow down, however if the final weighted input to a ReLU neuron is negative, the gradient vanishes (goes to zero), and so the ReLU neuron will also stop learning altogether. These imperfections have spawned a plethora of alternate greyscale conversion functions which can be employed ad hoc as needed for particular AI tasks.⁴

因此，在 sigmoid、tanh、ReLU 和其他函数中进行选择是一项练习，首先要用最简单的实现方式解决手头的任务，然后当问题出现时，通常通过反复试验找到最佳的纠正函数和程序。当需要提高分类和预测准确性时，可以调用算法调整、不同的成本函数来增强收敛、超参数化等，同时要考虑计算负担。程序选择通常是根据哪种方法最有效而做出的，而不一定完全理解为什么某些方法比其他方法更有效。

Choosing among sigmoid, tanh, ReLU, and others thus is an exercise in first addressing the task at hand in its simplest implementation, and then as problems arise, finding the best corrective functions and procedures, usually by trial and error. When improved classification and prediction accuracy are required, algorithm tuning, different cost functions to enhance convergence, hyperparameteration, and so can be called on, all the while keeping in mind computational burden. Procedural choices often are made by just going with what works best and not necessarily completely understanding why something works better than something else.

人工神经元激活水平的参数化为动态调整突触模式以提取特征提供了一种手段，但究竟如何调整权重和偏差，使得人工神经网络能够学习，从而表现出人工智能呢？

The parameterization of the artificial neuron activation levels provides a means for dynamic adjustment of synaptic patterns for feature extraction, but how exactly are the weights and biases adjusted so that the artificial neural network can learn, and thus exhibit artificial intelligence?

一个n 人工神经网络 (ANN) 必须经过训练才能识别物体和数据，年轻的 ANN 正在学习如何通过呈现图像和数据集进行识别。神经元激活水平最初由权重和偏差的正态分布参数化，因此她的神经网络是一张空白画布，她已准备好进行^机器学习。1

An artificial neural network (ANN) must be trained to recognize objects and data, young ANN is learning how to recognize by being presented with training sets of images and data. The neuron activation levels have been parameterized initially by a Normal distribution of weights and biases, her neural network is thus a blank canvas, she is ready to machine learn.¹

她最初的随机人工神经激活水平分布和训练集数据之间的差异自然会很大，她的学习任务就是减少这种差异，以便提取训练集图像和数据的特征，并将其存储在内存中，以便识别呈现给她的图像和数据。该差异由损失函数量化，表示为L层决策行向量神经元输出的激活水平与训练集y向量²之间的差异的平方和

The difference between her initial random artificial neural activation level distribution and the training set data naturally will be quite large, her learning task then is to reduce that difference in order to extract features characteristic of the training set images and data to store in memory in order to recognize images and data presented to her. That difference is quantified by a Loss Function, expressed by the sum of the squares of the differences between the outputted activation levels of the decisional row vector neurons in layer L and the training set y vector,²

就像人工智能中所使用的那样，对所有的损失取平均值对训练集中所有m 个样本进行函数计算得出平均成本函数；它包括对训练集中所有样本i求平均的网络中的所有权重和所有偏差。

As employed in artificial intelligence, taking the average of all of the Loss Functions over all the m samples in the training set gives the Average Cost Function; it comprises all the weights and all the biases in the network averaged over all the samples i in the training set.

平均成本函数$\overline{碳}$是经济学中的一个术语，表示低效生产的成本，因此C可以被认为是与训练集匹配的错误成本，所以平均成本函数的最小化将减少 ANN 的神经元激活模式和训练集之间的差异。

The Average Cost Function $\overline{C}$ is a term taken from economics as the cost of inefficient production, thus C can be thought of just the Cost of Being Wrong in regard to matching the training set, so the minimization of the Average Cost function will reduce the differences between ANN's neuron activation patterns and the training set.

计算平均成本函数不会像依次计算每个训练集示例的损失函数那样繁重，并且有人指出，取平均值将有助于平均掉数据中可能存在的噪声和不相关因素。

Calculating the Average Cost Function will not be as computationally burdensome as calculating the Loss Function of each training set example in turn, and it is noted by some that taking the average will beneficially average out noise and irrelevant factors that may be in the data.

平均成本函数定义为，³

The Average Cost Function then is defined as,³

回想一下第 15章

where recall from Chapter 15 that

在初等微积分中，可以轻松地最小化单个变量的任何连续可微函数，方法是对该变量求导数并将其设置为零，以找到斜率水平的位置（即零斜率），这是凹曲线的最小点。

In elementary calculus, minimization of any continuous and differentiable function of a single variable is easily done by taking the derivative with respect to that variable and setting it equal to zero to find where the slope is horizontal (that is zero slope), which is the minimum point of a concave curve.

用C表示任何成本函数，二次函数C是连续且可微的，因此可以最小化，例如关于加权因子变量w，

Taking C to represent any Cost Function, a quadratic C is continuous and differentiable, so it can be minimized, for example with respect to a weighting factor variable w,

要找到权重变量w 的最小点，请随机选择曲线上的一个点，并确定要朝哪个方向移动才能到达Cw曲线上的最小点。这个方向是由所选点的曲线斜率符号给出；类比为在平均成本函数曲线上滚动的球，如果斜率为正，它将向左滚动，如果斜率为负，它将向右滚动，速度取决于斜率的严重程度。如果滚动速度不是太快，它将在水平斜率最小处停止，从而确定最小成本。

To find the minimum point with respect to a weighting variable w, randomly choose a point on the curve, and determine what direction to move in order to reach the minimum point on the C-w curve. This direction is given by the sign of the slope of the curve at that chosen point; the analogy is a ball rolling on the Average Cost Function curve, it will roll left if the slope is positive and right if the slope is negative, and with a speed depending on the severity of the slope. If not rolling too fast, it will stop at the horizontal slope minimum, thereby determining a minimum Cost.

这给出了一个线索，即最好使用向量来描述此操作，因为它既有大小又有方向。从平均成本函数与加权变量曲线上随机选择的点开始，随着接近最小点，由于斜率的绝对值减小，滚动球的速度减慢，学习算法可以相应地减小球的步长，以防止无意中超过最小点。

This gives the clue that this operation would be best described using a vector since it has both magnitude and direction. From a randomly chosen point on the Average Cost Function versus weighting variable curve, as the minimum point is approached, since the absolute value of the slope decreases and the rolling ball slows down, the learning algorithm can accordingly reduce the step size of the ball to prevent inadvertently overshooting the minimum point.

不幸的是，关于变量w 的成本曲线可能有许多凹度，因此有多个局部最小值，也包括凸曲线最大值（斜率也为零），如下图左所示，并且除非找到全局最小值（即平均成本函数的绝对最小值，而不仅仅是局部最小值），否则成本不会关于特定权重变量最小化。在寻找全局最小值时遇到局部最小值的问题自人工智能研究诞生以来就一直困扰着它。

Unfortunately, the Cost curve with respect to the variable w may have many concavities and therefore multiple local minima and also include convex curve maxima (that also have zero slope) as shown in the figure below at left, and the Cost will not be minimized with respect to a particular weighting variable unless the global minimum, meaning the absolute minimum of the Average Cost Function, and not just a local minima, is found. The problem of encountering local minima in the search for the global minimum has plagued artificial intelligence research since its inception.

如果要确定两个变量权重的成本函数的最小化，则将不再使用Cw曲线，而是使用成本函数与权重的三维轮廓线，如下图右所示，其中有一个滚动球在寻找轮廓线的最小值，

If the minimization of the Cost Function for two variable weights is to be determined, instead of C-w curves there will be a three-dimensional contour of Cost Function versus weights as shown in the figure below at right, with a rolling ball searching for the minimum of the contour,

只需查看计算机生成的Cw图，就可以找到二维和三维模型的局部和全局最小值，但是人工神经网络通常具有很多权重和偏差参数，因此成本将是很多变量的函数，并且任何大于三维的轮廓都是不可能可视化的。

Local and global minima for two-dimensional and three-dimensional models can be found by simply looking at the computer-generated C-w plots, but artificial neural networks usually have many, many weight and bias parameters, so the Cost will be a function of many, many variables, and any contour of greater than three-dimensions is impossible to visualize.

虽然人类无法在三维以上进行物理可视化，但他们可以在概念上用心灵之眼进行观察，幸运的是，计算机可以在几乎无限的维度上运行，因此可以通过查找向量分析的梯度来计算任意数量变量的成本函数最小化。梯度是一个表示最陡下降方向的向量，其幅度是多维轮廓陡度的度量，为了找到最小值，它将是一个梯度下降，因此是一个负梯度向量，

Although humans cannot physically visualize in greater than three dimensions, they can conceptually view with the mind's eye, and fortunately the computer can operate in almost infinite dimensions, and so the computation of Cost Function minimization with respect to any number of variables can be performed by finding the gradient of vector analysis. The gradient is a vector representing the direction of steepest descent, with a magnitude that is a measure of the steepness of the multidimensional contour, and for finding a minimum it will be a gradient descent and thus a negative gradient vector,

以三维加权变量为例，对成本函数C进行梯度运算，

The gradient operating on the Cost Function C in an example for just the weighting variables in three dimensions is,